home *** CD-ROM | disk | FTP | other *** search
| Unknown | 1996-08-29 | 24.9 KB |
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MacOS 8.1
|
Win98
|
DOS
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| Confidence | Program | Detection | Match Type | Support
|
|---|
| 1%
| dexvert
| Eclipse Tutorial (other/eclipseTutorial)
| ext
| Unsupported |
| 1%
| dexvert
| JuggleKrazy Tutorial (other/juggleKrazyTutorial)
| ext
| Unsupported |
| 100%
| file
| data
| default
| |
| 100%
| gt2
| Kopftext: 'TUTOR 06'
| default (weak)
|
|
hex view+--------+-------------------------+-------------------------+--------+--------+
|00000000| 54 55 54 4f 52 20 30 36 | bc 5b 00 00 c0 07 00 00 |TUTOR 06|.[......|
|00000010| 00 17 4f 04 0d 0b 00 57 | 72 6f 6e 67 2e 20 20 57 |..O....W|rong. W|
|00000020| 65 20 73 6f 6c 76 65 20 | 74 68 65 20 70 72 6f 62 |e solve |the prob|
|00000030| 6c 65 6d 20 61 73 20 66 | 6f 6c 6c 6f 77 73 2e 12 |lem as f|ollows..|
|00000040| 30 0d 0a 00 0d 0b 00 20 | 20 20 20 20 28 31 35 20 |0...... | (15 |
|00000050| 2b 20 31 30 11 33 69 11 | 31 29 20 2d 20 28 32 20 |+ 10.3i.|1) - (2 |
|00000060| 2b 20 31 30 11 33 69 11 | 31 29 20 3d 20 28 31 35 |+ 10.3i.|1) = (15|
|00000070| 20 2d 20 32 29 20 2b 20 | 28 31 30 20 2d 20 31 30 | - 2) + |(10 - 10|
|00000080| 29 11 33 69 20 11 31 3d | 20 31 33 0d 0a 00 00 17 |).3i .1=| 13.....|
|00000090| 4f 04 0d 0b 00 52 69 67 | 68 74 2e 20 20 41 66 74 |O....Rig|ht. Aft|
|000000a0| 65 72 20 73 75 62 74 72 | 61 63 74 69 6e 67 20 74 |er subtr|acting t|
|000000b0| 68 65 20 74 77 6f 20 63 | 6f 6d 70 6c 65 78 20 6e |he two c|omplex n|
|000000c0| 75 6d 62 65 72 73 2c 20 | 77 65 20 6f 62 74 61 69 |umbers, |we obtai|
|000000d0| 6e 20 74 68 65 20 72 65 | 61 6c 20 0d 0a 00 6e 75 |n the re|al ...nu|
|000000e0| 6d 62 65 72 20 31 33 2e | 0d 0a 00 00 17 4f 04 0d |mber 13.|.....O..|
|000000f0| 0b 00 57 72 6f 6e 67 2e | 20 20 57 65 20 73 6f 6c |..Wrong.| We sol|
|00000100| 76 65 20 74 68 65 20 70 | 72 6f 62 6c 65 6d 20 61 |ve the p|roblem a|
|00000110| 73 20 66 6f 6c 6c 6f 77 | 73 2e 12 30 0d 0a 00 0d |s follow|s..0....|
|00000120| 0b 00 20 20 20 20 20 28 | 31 35 20 2b 20 31 30 11 |.. (|15 + 10.|
|00000130| 33 69 11 31 29 20 2d 20 | 28 32 20 2b 20 31 30 11 |3i.1) - |(2 + 10.|
|00000140| 33 69 11 31 29 20 3d 20 | 28 31 35 20 2d 20 32 29 |3i.1) = |(15 - 2)|
|00000150| 20 2b 20 28 31 30 20 2d | 20 31 30 29 11 33 69 20 | + (10 -| 10).3i |
|00000160| 11 31 3d 20 31 33 0d 0a | 00 00 17 4f 04 0d 0b 00 |.1= 13..|...O....|
|00000170| 57 72 6f 6e 67 2e 20 20 | 57 65 20 73 6f 6c 76 65 |Wrong. |We solve|
|00000180| 20 74 68 65 20 70 72 6f | 62 6c 65 6d 20 61 73 20 | the pro|blem as |
|00000190| 66 6f 6c 6c 6f 77 73 2e | 12 30 0d 0a 00 0d 0b 00 |follows.|.0......|
|000001a0| 20 20 20 20 20 28 31 35 | 20 2b 20 31 30 11 33 69 | (15| + 10.3i|
|000001b0| 11 31 29 20 2d 20 28 32 | 20 2b 20 31 30 11 33 69 |.1) - (2| + 10.3i|
|000001c0| 11 31 29 20 3d 20 28 31 | 35 20 2d 20 32 29 20 2b |.1) = (1|5 - 2) +|
|000001d0| 20 28 31 30 20 2d 20 31 | 30 29 11 33 69 20 11 31 | (10 - 1|0).3i .1|
|000001e0| 3d 20 31 33 0d 0a 00 00 | 17 4f 06 20 20 20 20 20 |= 13....|.O. |
|000001f0| 20 20 20 20 20 20 20 20 | 20 20 20 20 20 20 20 20 | | |
|00000200| 11 34 44 32 32 20 20 20 | 20 20 20 20 20 20 20 20 |.4D22 | |
|00000210| 20 20 20 20 20 20 20 20 | 20 20 20 20 20 20 20 20 | | |
|00000220| 20 20 20 20 20 20 20 44 | 32 0d 0b 00 11 31 57 72 | D|2....1Wr|
|00000230| 6f 6e 67 2e 20 20 57 72 | 69 74 69 6e 67 20 31 20 |ong. Wr|iting 1 |
|00000240| 2b 20 11 34 53 20 11 31 | 2d 33 20 69 6e 20 73 74 |+ .4S .1|-3 in st|
|00000250| 61 6e 64 61 72 64 20 66 | 6f 72 6d 2c 20 77 65 20 |andard f|orm, we |
|00000260| 6f 62 74 61 69 6e 20 31 | 20 2b 20 11 34 53 20 11 |obtain 1| + .4S .|
|00000270| 31 33 11 33 69 11 31 2e | 20 20 54 68 75 73 2c 20 |13.3i.1.| Thus, |
|00000280| 74 68 65 20 0d 0a 00 20 | 20 20 20 20 20 20 20 20 |the ... | |
|00000290| 20 20 20 20 20 20 20 20 | 20 11 34 44 32 0d 0b 00 | | .4D2...|
|000002a0| 11 31 63 6f 6e 6a 75 67 | 61 74 65 20 69 73 20 31 |.1conjug|ate is 1|
|000002b0| 20 2d 20 11 34 53 20 11 | 31 33 11 33 69 11 31 2e | - .4S .|13.3i.1.|
|000002c0| 20 20 4e 6f 77 2c 20 66 | 69 6e 69 73 68 20 74 68 | Now, f|inish th|
|000002d0| 65 20 70 72 6f 62 6c 65 | 6d 20 62 79 20 66 69 6e |e proble|m by fin|
|000002e0| 64 69 6e 67 20 74 68 65 | 20 70 72 6f 64 75 63 74 |ding the| product|
|000002f0| 20 6f 66 0d 0a 00 20 20 | 20 20 20 11 34 44 32 20 | of... | .4D2 |
|00000300| 20 20 20 20 20 20 20 20 | 20 20 44 32 0d 0b 00 11 | | D2....|
|00000310| 31 31 20 2b 20 11 34 53 | 20 11 31 33 11 33 69 20 |11 + .4S| .13.3i |
|00000320| 11 31 61 6e 64 20 31 20 | 2d 20 11 34 53 20 11 31 |.1and 1 |- .4S .1|
|00000330| 33 11 33 69 11 31 2e 0d | 0a 00 00 17 4f 04 0d 0b |3.3i.1..|....O...|
|00000340| 00 57 72 6f 6e 67 2e 20 | 20 57 65 20 66 69 6e 64 |.Wrong. | We find|
|00000350| 20 74 68 65 20 70 72 6f | 64 75 63 74 20 61 73 20 | the pro|duct as |
|00000360| 66 6f 6c 6c 6f 77 73 2e | 12 30 0d 0a 00 20 20 20 |follows.|.0... |
|00000370| 20 20 20 20 20 20 20 20 | 11 34 44 32 20 20 20 20 | |.4D2 |
|00000380| 20 20 20 20 44 32 20 20 | 20 20 20 20 11 32 32 20 | D2 | .22 |
|00000390| 20 20 20 20 11 34 44 32 | 20 11 32 32 0d 0b 00 20 | .4D2| .22... |
|000003a0| 20 20 20 20 11 31 28 31 | 20 2b 20 11 34 53 20 11 | .1(1| + .4S .|
|000003b0| 31 33 11 33 69 11 31 29 | 28 31 20 2d 20 11 34 53 |13.3i.1)|(1 - .4S|
|000003c0| 20 11 31 33 11 33 69 11 | 31 29 20 3d 20 31 20 20 | .13.3i.|1) = 1 |
|000003d0| 2b 20 28 11 34 53 20 11 | 31 33 29 20 20 3d 20 31 |+ (.4S .|13) = 1|
|000003e0| 20 2b 20 33 20 3d 20 34 | 0d 0a 00 00 17 4f 06 20 | + 3 = 4|.....O. |
|000003f0| 20 20 20 20 20 20 20 20 | 20 20 20 20 20 20 20 20 | | |
|00000400| 20 20 20 20 11 34 44 32 | 32 20 20 20 20 20 20 20 | .4D2|2 |
|00000410| 20 20 20 20 20 20 20 20 | 20 20 20 20 20 20 20 20 | | |
|00000420| 20 20 20 20 20 20 20 20 | 20 20 20 44 32 0d 0b 00 | | D2...|
|00000430| 11 31 57 72 6f 6e 67 2e | 20 20 57 72 69 74 69 6e |.1Wrong.| Writin|
|00000440| 67 20 31 20 2b 20 11 34 | 53 20 11 31 2d 33 20 69 |g 1 + .4|S .1-3 i|
|00000450| 6e 20 73 74 61 6e 64 61 | 72 64 20 66 6f 72 6d 2c |n standa|rd form,|
|00000460| 20 77 65 20 6f 62 74 61 | 69 6e 20 31 20 2b 20 11 | we obta|in 1 + .|
|00000470| 34 53 20 11 31 33 11 33 | 69 11 31 2e 20 20 54 68 |4S .13.3|i.1. Th|
|00000480| 75 73 2c 20 74 68 65 20 | 0d 0a 00 20 20 20 20 20 |us, the |... |
|00000490| 20 20 20 20 20 20 20 20 | 20 20 20 20 20 11 34 44 | | .4D|
|000004a0| 32 0d 0b 00 11 31 63 6f | 6e 6a 75 67 61 74 65 20 |2....1co|njugate |
|000004b0| 69 73 20 31 20 2d 20 11 | 34 53 20 11 31 33 11 33 |is 1 - .|4S .13.3|
|000004c0| 69 11 31 2e 20 20 4e 6f | 77 2c 20 66 69 6e 69 73 |i.1. No|w, finis|
|000004d0| 68 20 74 68 65 20 70 72 | 6f 62 6c 65 6d 20 62 79 |h the pr|oblem by|
|000004e0| 20 66 69 6e 64 69 6e 67 | 20 74 68 65 20 70 72 6f | finding| the pro|
|000004f0| 64 75 63 74 20 6f 66 0d | 0a 00 20 20 20 20 20 11 |duct of.|.. .|
|00000500| 34 44 32 20 20 20 20 20 | 20 20 20 20 20 20 44 32 |4D2 | D2|
|00000510| 0d 0b 00 11 31 31 20 2b | 20 11 34 53 20 11 31 33 |....11 +| .4S .13|
|00000520| 11 33 69 20 11 31 61 6e | 64 20 31 20 2d 20 11 34 |.3i .1an|d 1 - .4|
|00000530| 53 20 11 31 33 11 33 69 | 11 31 2e 0d 0a 00 00 17 |S .13.3i|.1......|
|00000540| 4f 03 20 20 20 20 20 20 | 20 20 20 20 20 20 20 20 |O. | |
|00000550| 20 20 20 20 20 20 20 20 | 20 20 20 20 20 20 20 20 | | |
|00000560| 11 34 44 32 32 20 20 20 | 20 20 20 20 20 20 44 32 |.4D22 | D2|
|00000570| 0d 0b 00 11 31 52 69 67 | 68 74 2e 20 20 54 68 65 |....1Rig|ht. The|
|00000580| 20 63 6f 6e 6a 75 67 61 | 74 65 20 6f 66 20 31 20 | conjuga|te of 1 |
|00000590| 2b 20 11 34 53 20 11 31 | 2d 33 20 69 73 20 31 20 |+ .4S .1|-3 is 1 |
|000005a0| 2d 20 11 34 53 20 11 31 | 33 11 33 69 20 11 31 61 |- .4S .1|3.3i .1a|
|000005b0| 6e 64 20 74 68 65 69 72 | 20 70 72 6f 64 75 63 74 |nd their| product|
|000005c0| 20 69 73 20 34 2e 0d 0a | 00 00 17 4f 04 0d 0b 00 | is 4...|...O....|
|000005d0| 57 72 6f 6e 67 2e 20 20 | 54 68 65 20 63 6f 6e 6a |Wrong. |The conj|
|000005e0| 75 67 61 74 65 20 6f 66 | 20 31 30 11 33 69 20 11 |ugate of| 10.3i .|
|000005f0| 31 69 73 20 2d 31 30 11 | 33 69 11 31 2e 20 20 4e |1is -10.|3i.1. N|
|00000600| 6f 77 2c 20 66 69 6e 69 | 73 68 20 74 68 65 20 70 |ow, fini|sh the p|
|00000610| 72 6f 62 6c 65 6d 20 62 | 79 20 66 69 6e 64 69 6e |roblem b|y findin|
|00000620| 67 0d 0a 00 74 68 65 20 | 70 72 6f 64 75 63 74 20 |g...the |product |
|00000630| 6f 66 20 31 30 11 33 69 | 20 11 31 61 6e 64 20 2d |of 10.3i| .1and -|
|00000640| 31 30 11 33 69 11 31 2e | 0d 0a 00 00 17 4f 04 0d |10.3i.1.|.....O..|
|00000650| 0b 00 57 72 6f 6e 67 2e | 20 20 54 68 65 20 63 6f |..Wrong.| The co|
|00000660| 6e 6a 75 67 61 74 65 20 | 6f 66 20 31 30 11 33 69 |njugate |of 10.3i|
|00000670| 20 11 31 69 73 20 2d 31 | 30 11 33 69 11 31 2e 20 | .1is -1|0.3i.1. |
|00000680| 20 4e 6f 77 2c 20 66 69 | 6e 69 73 68 20 74 68 65 | Now, fi|nish the|
|00000690| 20 70 72 6f 62 6c 65 6d | 20 62 79 20 66 69 6e 64 | problem| by find|
|000006a0| 69 6e 67 0d 0a 00 74 68 | 65 20 70 72 6f 64 75 63 |ing...th|e produc|
|000006b0| 74 20 6f 66 20 31 30 11 | 33 69 20 11 31 61 6e 64 |t of 10.|3i .1and|
|000006c0| 20 2d 31 30 11 33 69 11 | 31 2e 0d 0a 00 00 17 4f | -10.3i.|1......O|
|000006d0| 04 0d 0b 00 57 72 6f 6e | 67 2e 20 20 57 65 20 66 |....Wron|g. We f|
|000006e0| 69 6e 64 20 74 68 65 20 | 70 72 6f 64 75 63 74 20 |ind the |product |
|000006f0| 6f 66 20 31 30 11 33 69 | 20 11 31 61 6e 64 20 2d |of 10.3i| .1and -|
|00000700| 31 30 11 33 69 20 11 31 | 61 73 20 66 6f 6c 6c 6f |10.3i .1|as follo|
|00000710| 77 73 2e 12 30 0d 0a 00 | 20 20 20 20 20 20 20 20 |ws..0...| |
|00000720| 20 20 20 20 20 20 20 20 | 20 20 20 20 20 20 20 20 | | |
|00000730| 11 32 32 0d 0b 00 20 20 | 20 20 20 11 31 28 31 30 |.22... | .1(10|
|00000740| 11 33 69 11 31 29 28 2d | 31 30 11 33 69 11 31 29 |.3i.1)(-|10.3i.1)|
|00000750| 20 3d 20 2d 31 30 30 11 | 33 69 20 20 11 31 3d 20 | = -100.|3i .1= |
|00000760| 2d 31 30 30 28 2d 31 29 | 20 3d 20 31 30 30 0d 0a |-100(-1)| = 100..|
|00000770| 00 00 17 4f 03 0d 0b 00 | 52 69 67 68 74 2e 20 20 |...O....|Right. |
|00000780| 54 68 65 20 63 6f 6e 6a | 75 67 61 74 65 20 6f 66 |The conj|ugate of|
|00000790| 20 31 30 11 33 69 20 11 | 31 69 73 20 2d 31 30 11 | 10.3i .|1is -10.|
|000007a0| 33 69 20 11 31 61 6e 64 | 20 74 68 65 69 72 20 70 |3i .1and| their p|
|000007b0| 72 6f 64 75 63 74 20 69 | 73 20 31 30 30 2e 0d 0a |roduct i|s 100...|
|000007c0| 00 00 17 4f 09 0d 0b 00 | 57 72 6f 6e 67 2e 20 20 |...O....|Wrong. |
|000007d0| 57 65 20 73 6f 6c 76 65 | 20 74 68 65 20 70 72 6f |We solve| the pro|
|000007e0| 62 6c 65 6d 20 61 73 20 | 66 6f 6c 6c 6f 77 73 2e |blem as |follows.|
|000007f0| 20 20 20 12 30 0d 0a 00 | 0d 0b 00 20 20 11 34 44 | .0...|... .4D|
|00000800| 32 32 20 20 44 32 32 20 | 20 20 20 44 32 32 20 20 |22 D22 | D22 |
|00000810| 20 20 20 44 32 20 20 20 | 44 32 0d 0b 00 20 53 20 | D2 |D2... S |
|00000820| 11 31 2d 33 28 11 34 53 | 20 11 31 2d 33 20 2b 20 |.1-3(.4S| .1-3 + |
|00000830| 11 34 53 20 11 31 2d 34 | 29 20 3d 20 11 34 53 20 |.4S .1-4|) = .4S |
|00000840| 11 31 33 11 33 69 11 31 | 28 11 34 53 20 11 31 33 |.13.3i.1|(.4S .13|
|00000850| 11 33 69 20 11 31 2b 20 | 32 11 33 69 11 31 29 20 |.3i .1+ |2.3i.1) |
|00000860| 20 20 20 20 20 20 20 20 | 20 20 20 20 20 20 20 20 | | |
|00000870| 11 32 12 31 57 72 69 74 | 65 20 69 6e 20 73 74 61 |.2.1Writ|e in sta|
|00000880| 6e 64 61 72 64 20 66 6f | 72 6d 12 30 0d 0a 00 20 |ndard fo|rm.0... |
|00000890| 20 20 20 20 20 20 20 20 | 20 20 20 20 20 20 20 20 | | |
|000008a0| 20 20 20 20 20 20 20 11 | 34 44 32 20 20 20 20 44 | .|4D2 D|
|000008b0| 32 20 20 20 20 20 20 20 | 44 32 0d 0b 00 20 20 20 |2 |D2... |
|000008c0| 20 20 20 20 20 20 20 20 | 20 20 20 20 20 20 20 20 | | |
|000008d0| 20 11 31 3d 20 28 11 34 | 53 20 11 31 33 11 33 69 | .1= (.4|S .13.3i|
|000008e0| 11 31 29 28 11 34 53 20 | 11 31 33 11 33 69 11 31 |.1)(.4S |.13.3i.1|
|000008f0| 29 20 2b 20 28 11 34 53 | 20 11 31 33 11 33 69 11 |) + (.4S| .13.3i.|
|00000900| 31 29 28 32 11 33 69 11 | 31 29 20 20 20 20 20 20 |1)(2.3i.|1) |
|00000910| 11 32 12 31 44 69 73 74 | 72 69 62 75 74 69 76 65 |.2.1Dist|ributive|
|00000920| 20 50 72 6f 70 65 72 74 | 79 12 30 0d 0a 00 20 20 | Propert|y.0... |
|00000930| 20 20 20 20 20 20 20 20 | 20 20 20 20 20 20 20 20 | | |
|00000940| 20 20 20 20 20 20 20 20 | 20 20 20 20 20 20 20 11 | | .|
|00000950| 34 44 32 0d 0b 00 20 20 | 20 20 20 20 20 20 20 20 |4D2... | |
|00000960| 20 20 20 20 20 20 20 20 | 20 20 11 31 3d 20 33 28 | | .1= 3(|
|00000970| 2d 31 29 20 2b 20 32 28 | 11 34 53 20 11 31 33 29 |-1) + 2(|.4S .13)|
|00000980| 28 2d 31 29 0d 0a 00 20 | 20 20 20 20 20 20 20 20 |(-1)... | |
|00000990| 20 20 20 20 20 20 20 20 | 20 20 20 20 20 20 20 20 | | |
|000009a0| 20 20 20 20 11 34 44 32 | 0d 0b 00 20 20 20 20 20 | .4D2|... |
|000009b0| 20 20 20 20 20 20 20 20 | 20 20 20 20 20 20 20 11 | | .|
|000009c0| 31 3d 20 2d 33 20 2d 20 | 32 11 34 53 20 11 31 33 |1= -3 - |2.4S .13|
|000009d0| 20 20 20 20 20 20 20 20 | 20 20 20 20 20 20 20 20 | | |
|000009e0| 20 20 20 20 20 20 11 32 | 12 31 53 69 6d 70 6c 69 | .2|.1Simpli|
|000009f0| 66 69 65 64 20 66 6f 72 | 6d 12 30 0d 0a 00 00 17 |fied for|m.0.....|
|00000a00| 4f 09 0d 0b 00 57 72 6f | 6e 67 2e 20 20 57 65 20 |O....Wro|ng. We |
|00000a10| 73 6f 6c 76 65 20 74 68 | 65 20 70 72 6f 62 6c 65 |solve th|e proble|
|00000a20| 6d 20 61 73 20 66 6f 6c | 6c 6f 77 73 2e 20 20 20 |m as fol|lows. |
|00000a30| 12 30 0d 0a 00 0d 0b 00 | 20 20 11 34 44 32 32 20 |.0......| .4D22 |
|00000a40| 20 44 32 32 20 20 20 20 | 44 32 32 20 20 20 20 20 | D22 |D22 |
|00000a50| 44 32 20 20 20 44 32 0d | 0b 00 20 53 20 11 31 2d |D2 D2.|.. S .1-|
|00000a60| 33 28 11 34 53 20 11 31 | 2d 33 20 2b 20 11 34 53 |3(.4S .1|-3 + .4S|
|00000a70| 20 11 31 2d 34 29 20 3d | 20 11 34 53 20 11 31 33 | .1-4) =| .4S .13|
|00000a80| 11 33 69 11 31 28 11 34 | 53 20 11 31 33 11 33 69 |.3i.1(.4|S .13.3i|
|00000a90| 20 11 31 2b 20 32 11 33 | 69 11 31 29 20 20 20 20 | .1+ 2.3|i.1) |
|00000aa0| 20 20 20 20 20 20 20 20 | 20 20 20 20 20 11 32 12 | | .2.|
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|00000ac0| 72 64 20 66 6f 72 6d 12 | 30 0d 0a 00 20 20 20 20 |rd form.|0... |
|00000ad0| 20 20 20 20 20 20 20 20 | 20 20 20 20 20 20 20 20 | | |
|00000ae0| 20 20 20 20 11 34 44 32 | 20 20 20 20 44 32 20 20 | .4D2| D2 |
|00000af0| 20 20 20 20 20 44 32 0d | 0b 00 20 20 20 20 20 20 | D2.|.. |
|00000b00| 20 20 20 20 20 20 20 20 | 20 20 20 20 20 20 11 31 | | .1|
|00000b10| 3d 20 28 11 34 53 20 11 | 31 33 11 33 69 11 31 29 |= (.4S .|13.3i.1)|
|00000b20| 28 11 34 53 20 11 31 33 | 11 33 69 11 31 29 20 2b |(.4S .13|.3i.1) +|
|00000b30| 20 28 11 34 53 20 11 31 | 33 11 33 69 11 31 29 28 | (.4S .1|3.3i.1)(|
|00000b40| 32 11 33 69 11 31 29 20 | 20 20 20 20 20 11 32 12 |2.3i.1) | .2.|
|00000b50| 31 44 69 73 74 72 69 62 | 75 74 69 76 65 20 50 72 |1Distrib|utive Pr|
|00000b60| 6f 70 65 72 74 79 12 30 | 0d 0a 00 20 20 20 20 20 |operty.0|... |
|00000b70| 20 20 20 20 20 20 20 20 | 20 20 20 20 20 20 20 20 | | |
|00000b80| 20 20 20 20 20 20 20 20 | 20 20 20 20 11 34 44 32 | | .4D2|
|00000b90| 0d 0b 00 20 20 20 20 20 | 20 20 20 20 20 20 20 20 |... | |
|00000ba0| 20 20 20 20 20 20 20 11 | 31 3d 20 33 28 2d 31 29 | .|1= 3(-1)|
|00000bb0| 20 2b 20 32 28 11 34 53 | 20 11 31 33 29 28 2d 31 | + 2(.4S| .13)(-1|
|00000bc0| 29 0d 0a 00 20 20 20 20 | 20 20 20 20 20 20 20 20 |)... | |
|00000bd0| 20 20 20 20 20 20 20 20 | 20 20 20 20 20 20 20 20 | | |
|00000be0| 20 11 34 44 32 0d 0b 00 | 20 20 20 20 20 20 20 20 | .4D2...| |
|00000bf0| 20 20 20 20 20 20 20 20 | 20 20 20 20 11 31 3d 20 | | .1= |
|00000c00| 2d 33 20 2d 20 32 11 34 | 53 20 11 31 33 20 20 20 |-3 - 2.4|S .13 |
|00000c10| 20 20 20 20 20 20 20 20 | 20 20 20 20 20 20 20 20 | | |
|00000c20| 20 20 20 11 32 12 31 53 | 69 6d 70 6c 69 66 69 65 | .2.1S|implifie|
|00000c30| 64 20 66 6f 72 6d 12 30 | 0d 0a 00 00 17 4f 09 0d |d form.0|.....O..|
|00000c40| 0b 00 57 72 6f 6e 67 2e | 20 20 57 65 20 73 6f 6c |..Wrong.| We sol|
|00000c50| 76 65 20 74 68 65 20 70 | 72 6f 62 6c 65 6d 20 61 |ve the p|roblem a|
|00000c60| 73 20 66 6f 6c 6c 6f 77 | 73 2e 20 20 20 12 30 0d |s follow|s. .0.|
|00000c70| 0a 00 0d 0b 00 20 20 11 | 34 44 32 32 20 20 44 32 |..... .|4D22 D2|
|00000c80| 32 20 20 20 20 44 32 32 | 20 20 20 20 20 44 32 20 |2 D22| D2 |
|00000c90| 20 20 44 32 0d 0b 00 20 | 53 20 11 31 2d 33 28 11 | D2... |S .1-3(.|
|00000ca0| 34 53 20 11 31 2d 33 20 | 2b 20 11 34 53 20 11 31 |4S .1-3 |+ .4S .1|
|00000cb0| 2d 34 29 20 3d 20 11 34 | 53 20 11 31 33 11 33 69 |-4) = .4|S .13.3i|
|00000cc0| 11 31 28 11 34 53 20 11 | 31 33 11 33 69 20 11 31 |.1(.4S .|13.3i .1|
|00000cd0| 2b 20 32 11 33 69 11 31 | 29 20 20 20 20 20 20 20 |+ 2.3i.1|) |
|00000ce0| 20 20 20 20 20 20 20 20 | 20 20 11 32 12 31 57 72 | | .2.1Wr|
|00000cf0| 69 74 65 20 69 6e 20 73 | 74 61 6e 64 61 72 64 20 |ite in s|tandard |
|00000d00| 66 6f 72 6d 12 30 0d 0a | 00 20 20 20 20 20 20 20 |form.0..|. |
|00000d10| 20 20 20 20 20 20 20 20 | 20 20 20 20 20 20 20 20 | | |
|00000d20| 20 11 34 44 32 20 20 20 | 20 44 32 20 20 20 20 20 | .4D2 | D2 |
|00000d30| 20 20 44 32 0d 0b 00 20 | 20 20 20 20 20 20 20 20 | D2... | |
|00000d40| 20 20 20 20 20 20 20 20 | 20 20 20 11 31 3d 20 28 | | .1= (|
|00000d50| 11 34 53 20 11 31 33 11 | 33 69 11 31 29 28 11 34 |.4S .13.|3i.1)(.4|
|00000d60| 53 20 11 31 33 11 33 69 | 11 31 29 20 2b 20 28 11 |S .13.3i|.1) + (.|
|00000d70| 34 53 20 11 31 33 11 33 | 69 11 31 29 28 32 11 33 |4S .13.3|i.1)(2.3|
|00000d80| 69 11 31 29 20 20 20 20 | 20 20 11 32 12 31 44 69 |i.1) | .2.1Di|
|00000d90| 73 74 72 69 62 75 74 69 | 76 65 20 50 72 6f 70 65 |stributi|ve Prope|
|00000da0| 72 74 79 12 30 0d 0a 00 | 20 20 20 20 20 20 20 20 |rty.0...| |
|00000db0| 20 20 20 20 20 20 20 20 | 20 20 20 20 20 20 20 20 | | |
|00000dc0| 20 20 20 20 20 20 20 20 | 20 11 34 44 32 0d 0b 00 | | .4D2...|
|00000dd0| 20 20 20 20 20 20 20 20 | 20 20 20 20 20 20 20 20 | | |
|00000de0| 20 20 20 20 11 31 3d 20 | 33 28 2d 31 29 20 2b 20 | .1= |3(-1) + |
|00000df0| 32 28 11 34 53 20 11 31 | 33 29 28 2d 31 29 0d 0a |2(.4S .1|3)(-1)..|
|00000e00| 00 20 20 20 20 20 20 20 | 20 20 20 20 20 20 20 20 |. | |
|00000e10| 20 20 20 20 20 20 20 20 | 20 20 20 20 20 20 11 34 | | .4|
|00000e20| 44 32 0d 0b 00 20 20 20 | 20 20 20 20 20 20 20 20 |D2... | |
|00000e30| 20 20 20 20 20 20 20 20 | 20 11 31 3d 20 2d 33 20 | | .1= -3 |
|00000e40| 2d 20 32 11 34 53 20 11 | 31 33 20 20 20 20 20 20 |- 2.4S .|13 |
|00000e50| 20 20 20 20 20 20 20 20 | 20 20 20 20 20 20 20 20 | | |
|00000e60| 11 32 12 31 53 69 6d 70 | 6c 69 66 69 65 64 20 66 |.2.1Simp|lified f|
|00000e70| 6f 72 6d 12 30 0d 0a 00 | 00 17 4f 03 20 20 20 20 |orm.0...|..O. |
|00000e80| 20 20 20 20 20 20 20 20 | 20 20 20 20 20 20 20 20 | | |
|00000e90| 20 20 20 20 20 20 20 20 | 20 20 20 20 20 20 20 20 | | |
|00000ea0| 20 20 20 20 20 20 20 11 | 34 44 32 0d 0b 00 11 31 | .|4D2....1|
|00000eb0| 52 69 67 68 74 2e 20 20 | 49 6e 20 73 69 6d 70 6c |Right. |In simpl|
|00000ec0| 65 73 74 20 66 6f 72 6d | 2c 20 77 65 20 6f 62 74 |est form|, we obt|
|00000ed0| 61 69 6e 20 2d 33 20 2d | 20 32 11 34 53 20 11 31 |ain -3 -| 2.4S .1|
|00000ee0| 33 2e 0d 0a 00 00 17 4f | 06 0d 0b 00 57 72 6f 6e |3......O|....Wron|
|00000ef0| 67 2e 20 20 57 65 20 73 | 6f 6c 76 65 20 74 68 65 |g. We s|olve the|
|00000f00| 20 70 72 6f 62 6c 65 6d | 20 61 73 20 66 6f 6c 6c | problem| as foll|
|00000f10| 6f 77 73 2e 12 30 0d 0a | 00 20 20 20 20 20 20 20 |ows..0..|. |
|00000f20| 20 20 20 20 20 20 20 20 | 20 20 20 20 20 20 20 20 | | |
|00000f30| 20 20 20 20 20 20 20 20 | 20 20 20 20 20 20 20 20 | | |
|00000f40| 20 20 20 20 20 11 32 32 | 0d 0b 00 20 20 20 11 31 | .22|... .1|
|00000f50| 28 34 20 2b 20 33 11 33 | 69 11 31 29 28 2d 37 20 |(4 + 3.3|i.1)(-7 |
|00000f60| 2b 20 34 11 33 69 11 31 | 29 20 3d 20 2d 32 38 20 |+ 4.3i.1|) = -28 |
|00000f70| 2b 20 31 36 11 33 69 20 | 11 31 2d 20 32 31 11 33 |+ 16.3i |.1- 21.3|
|00000f80| 69 20 11 31 2b 20 31 32 | 11 33 69 20 20 20 20 20 |i .1+ 12|.3i |
|00000f90| 20 20 20 20 11 32 12 31 | 46 4f 49 4c 20 4d 65 74 | .2.1|FOIL Met|
|00000fa0| 68 6f 64 12 30 0d 0a 00 | 20 20 20 20 20 20 20 20 |hod.0...| |
|00000fb0| 20 20 20 20 20 20 20 20 | 20 20 20 20 20 11 31 3d | | .1=|
|00000fc0| 20 2d 32 38 20 2b 20 31 | 32 28 2d 31 29 20 2b 20 | -28 + 1|2(-1) + |
|00000fd0| 31 36 11 33 69 20 11 31 | 2d 20 32 31 11 33 69 20 |16.3i .1|- 21.3i |
|00000fe0| 20 20 20 20 20 11 32 12 | 31 43 6f 6c 6c 65 63 74 | .2.|1Collect|
|00000ff0| 20 6c 69 6b 65 20 74 65 | 72 6d 73 12 30 0d 0a 00 | like te|rms.0...|
|00001000| 20 20 20 20 20 20 20 20 | 20 20 20 20 20 20 20 20 | | |
|00001010| 20 20 20 20 20 11 31 3d | 20 2d 34 30 20 2d 20 35 | .1=| -40 - 5|
|00001020| 11 33 69 20 20 20 20 20 | 20 20 20 20 20 20 20 20 |.3i | |
|00001030| 20 20 20 20 20 20 20 20 | 20 11 32 12 31 53 74 61 | | .2.1Sta|
|00001040| 6e 64 61 72 64 20 66 6f | 72 6d 12 30 0d 0a 00 00 |ndard fo|rm.0....|
|00001050| 17 4f 03 0d 0b 00 52 69 | 67 68 74 2e 20 20 55 73 |.O....Ri|ght. Us|
|00001060| 69 6e 67 20 74 68 65 20 | 46 4f 49 4c 20 4d 65 74 |ing the |FOIL Met|
|00001070| 68 6f 64 20 61 6e 64 20 | 73 69 6d 70 6c 69 66 79 |hod and |simplify|
|00001080| 69 6e 67 2c 20 77 65 20 | 6f 62 74 61 69 6e 20 2d |ing, we |obtain -|
|00001090| 34 30 20 2d 20 35 11 33 | 69 11 31 2e 0d 0a 00 00 |40 - 5.3|i.1.....|
|000010a0| 17 4f 06 0d 0b 00 57 72 | 6f 6e 67 2e 20 20 57 65 |.O....Wr|ong. We|
|000010b0| 20 73 6f 6c 76 65 20 74 | 68 65 20 70 72 6f 62 6c | solve t|he probl|
|000010c0| 65 6d 20 61 73 20 66 6f | 6c 6c 6f 77 73 2e 12 30 |em as fo|llows..0|
|000010d0| 0d 0a 00 20 20 20 20 20 | 20 20 20 20 20 20 20 20 |... | |
|000010e0| 20 20 20 20 20 20 20 20 | 20 20 20 20 20 20 20 20 | | |
|000010f0| 20 20 20 20 20 20 20 20 | 20 20 20 20 20 20 20 11 | | .|
|00001100| 32 32 0d 0b 00 20 20 20 | 11 31 28 34 20 2b 20 33 |22... |.1(4 + 3|
|00001110| 11 33 69 11 31 29 28 2d | 37 20 2b 20 34 11 33 69 |.3i.1)(-|7 + 4.3i|
|00001120| 11 31 29 20 3d 20 2d 32 | 38 20 2b 20 31 36 11 33 |.1) = -2|8 + 16.3|
|00001130| 69 20 11 31 2d 20 32 31 | 11 33 69 20 11 31 2b 20 |i .1- 21|.3i .1+ |
|00001140| 31 32 11 33 69 20 20 20 | 20 20 20 20 20 20 11 32 |12.3i | .2|
|00001150| 12 31 46 4f 49 4c 20 4d | 65 74 68 6f 64 12 30 0d |.1FOIL M|ethod.0.|
|00001160| 0a 00 20 20 20 20 20 20 | 20 20 20 20 20 20 20 20 |.. | |
|00001170| 20 20 20 20 20 20 20 11 | 31 3d 20 2d 32 38 20 2b | .|1= -28 +|
|00001180| 20 31 32 28 2d 31 29 20 | 2b 20 31 36 11 33 69 20 | 12(-1) |+ 16.3i |
|00001190| 11 31 2d 20 32 31 11 33 | 69 20 20 20 20 20 20 11 |.1- 21.3|i .|
|000011a0| 32 12 31 43 6f 6c 6c 65 | 63 74 20 6c 69 6b 65 20 |2.1Colle|ct like |
|000011b0| 74 65 72 6d 73 12 30 0d | 0a 00 20 20 20 20 20 20 |terms.0.|.. |
|000011c0| 20 20 20 20 20 20 20 20 | 20 20 20 20 20 20 20 11 | | .|
|000011d0| 31 3d 20 2d 34 30 20 2d | 20 35 11 33 69 20 20 20 |1= -40 -| 5.3i |
|000011e0| 20 20 20 20 20 20 20 20 | 20 20 20 20 20 20 20 20 | | |
|000011f0| 20 20 20 11 32 12 31 53 | 74 61 6e 64 61 72 64 20 | .2.1S|tandard |
|00001200| 66 6f 72 6d 12 30 0d 0a | 00 00 17 4f 06 0d 0b 00 |form.0..|...O....|
|00001210| 57 72 6f 6e 67 2e 20 20 | 57 65 20 73 6f 6c 76 65 |Wrong. |We solve|
|00001220| 20 74 68 65 20 70 72 6f | 62 6c 65 6d 20 61 73 20 | the pro|blem as |
|00001230| 66 6f 6c 6c 6f 77 73 2e | 12 30 0d 0a 00 20 20 20 |follows.|.0... |
|00001240| 20 20 20 20 20 20 20 20 | 20 20 20 20 20 20 20 20 | | |
|00001250| 20 20 20 20 20 20 20 20 | 20 20 20 20 20 20 20 20 | | |
|00001260| 20 20 20 20 20 20 20 20 | 20 11 32 32 0d 0b 00 20 | | .22... |
|00001270| 20 20 11 31 28 34 20 2b | 20 33 11 33 69 11 31 29 | .1(4 +| 3.3i.1)|
|00001280| 28 2d 37 20 2b 20 34 11 | 33 69 11 31 29 20 3d 20 |(-7 + 4.|3i.1) = |
|00001290| 2d 32 38 20 2b 20 31 36 | 11 33 69 20 11 31 2d 20 |-28 + 16|.3i .1- |
|000012a0| 32 31 11 33 69 20 11 31 | 2b 20 31 32 11 33 69 20 |21.3i .1|+ 12.3i |
|000012b0| 20 20 20 20 20 20 20 20 | 11 32 12 31 46 4f 49 4c | |.2.1FOIL|
|000012c0| 20 4d 65 74 68 6f 64 12 | 30 0d 0a 00 20 20 20 20 | Method.|0... |
|000012d0| 20 20 20 20 20 20 20 20 | 20 20 20 20 20 20 20 20 | | |
|000012e0| 20 11 31 3d 20 2d 32 38 | 20 2b 20 31 32 28 2d 31 | .1= -28| + 12(-1|
|000012f0| 29 20 2b 20 31 36 11 33 | 69 20 11 31 2d 20 32 31 |) + 16.3|i .1- 21|
|00001300| 11 33 69 20 20 20 20 20 | 20 11 32 12 31 43 6f 6c |.3i | .2.1Col|
|00001310| 6c 65 63 74 20 6c 69 6b | 65 20 74 65 72 6d 73 12 |lect lik|e terms.|
|00001320| 30 0d 0a 00 20 20 20 20 | 20 20 20 20 20 20 20 20 |0... | |
|00001330| 20 20 20 20 20 20 20 20 | 20 11 31 3d 20 2d 34 30 | | .1= -40|
|00001340| 20 2d 20 35 11 33 69 20 | 20 20 20 20 20 20 20 20 | - 5.3i | |
|00001350| 20 20 20 20 20 20 20 20 | 20 20 20 20 20 11 32 12 | | .2.|
|00001360| 31 53 74 61 6e 64 61 72 | 64 20 66 6f 72 6d 12 30 |1Standar|d form.0|
|00001370| 0d 0a 00 00 17 4f 03 0d | 0b 00 47 6f 6f 64 20 6a |.....O..|..Good j|
|00001380| 6f 62 2e 20 20 59 6f 75 | 20 64 65 74 65 72 6d 69 |ob. You| determi|
|00001390| 6e 65 64 20 11 33 61 20 | 11 31 61 6e 64 20 11 33 |ned .3a |.1and .3|
|000013a0| 62 20 11 31 63 6f 72 72 | 65 63 74 6c 79 2e 0d 0a |b .1corr|ectly...|
|000013b0| 00 00 17 4f 06 0d 0b 00 | 57 72 6f 6e 67 2e 20 20 |...O....|Wrong. |
|000013c0| 59 6f 75 20 64 65 74 65 | 72 6d 69 6e 65 64 20 11 |You dete|rmined .|
|000013d0| 33 61 20 11 31 63 6f 72 | 72 65 63 74 6c 79 2c 20 |3a .1cor|rectly, |
|000013e0| 62 75 74 20 11 33 62 20 | 11 34 3d 20 11 31 34 2e |but .3b |.4= .14.|
|000013f0| 20 20 54 6f 20 66 69 6e | 64 20 11 33 62 11 31 2c | To fin|d .3b.1,|
|00001400| 20 77 65 20 73 65 74 20 | 74 68 65 20 0d 0a 00 69 | we set |the ...i|
|00001410| 6d 61 67 69 6e 61 72 79 | 20 70 61 72 74 20 6f 66 |maginary| part of|
|00001420| 20 74 68 65 20 74 77 6f | 20 63 6f 6d 70 6c 65 78 | the two| complex|
|00001430| 20 6e 75 6d 62 65 72 73 | 20 65 71 75 61 6c 20 74 | numbers| equal t|
|00001440| 6f 20 65 61 63 68 20 6f | 74 68 65 72 20 61 6e 64 |o each o|ther and|
|00001450| 20 73 6f 6c 76 65 2e 12 | 30 0d 0a 00 0d 0b 00 20 | solve..|0...... |
|00001460| 20 20 20 20 11 33 62 20 | 11 31 2d 20 31 20 3d 20 | .3b |.1- 1 = |
|00001470| 2d 33 0d 0a 00 20 20 20 | 20 20 20 20 20 20 11 33 |-3... | .3|
|00001480| 62 20 11 31 3d 20 2d 32 | 0d 0a 00 00 17 4f 07 0d |b .1= -2|.....O..|
|00001490| 0b 00 57 72 6f 6e 67 2e | 20 20 46 6f 72 20 74 68 |..Wrong.| For th|
|000014a0| 65 73 65 20 74 77 6f 20 | 6e 75 6d 62 65 72 73 20 |ese two |numbers |
|000014b0| 74 6f 20 62 65 20 65 71 | 75 61 6c 2c 20 74 68 65 |to be eq|ual, the|
|000014c0| 69 72 20 72 65 61 6c 20 | 70 61 72 74 73 20 6d 75 |ir real |parts mu|
|000014d0| 73 74 20 62 65 20 65 71 | 75 61 6c 20 0d 0a 00 74 |st be eq|ual ...t|
|000014e0| 6f 20 65 61 63 68 20 6f | 74 68 65 72 20 61 6e 64 |o each o|ther and|
|000014f0| 20 74 68 65 69 72 20 69 | 6d 61 67 69 6e 61 72 79 | their i|maginary|
|00001500| 20 70 61 72 74 73 20 6d | 75 73 74 20 62 65 20 65 | parts m|ust be e|
|00001510| 71 75 61 6c 20 74 6f 20 | 65 61 63 68 20 6f 74 68 |qual to |each oth|
|00001520| 65 72 2e 20 20 54 68 75 | 73 2c 0d 0a 00 77 65 20 |er. Thu|s,...we |
|00001530| 63 61 6e 20 73 6f 6c 76 | 65 20 74 68 65 20 70 72 |can solv|e the pr|
|00001540| 6f 62 6c 65 6d 20 61 73 | 20 66 6f 6c 6c 6f 77 73 |oblem as| follows|
|00001550| 2e 12 30 0d 0a 00 0d 0b | 00 20 20 20 20 20 11 33 |..0.....|. .3|
|00001560| 61 20 11 31 2b 20 35 20 | 3d 20 37 20 20 20 20 20 |a .1+ 5 |= 7 |
|00001570| 61 6e 64 12 30 20 20 20 | 20 20 11 33 62 20 11 31 |and.0 | .3b .1|
|00001580| 2d 20 31 20 3d 20 2d 33 | 0d 0a 00 20 20 20 20 20 |- 1 = -3|... |
|00001590| 20 20 20 20 11 33 61 20 | 11 31 3d 20 32 20 20 20 | .3a |.1= 2 |
|000015a0| 20 20 20 20 20 20 20 20 | 20 20 20 20 20 20 11 33 | | .3|
|000015b0| 62 20 11 31 3d 20 2d 32 | 0d 0a 00 00 17 4f 07 0d |b .1= -2|.....O..|
|000015c0| 0b 00 57 72 6f 6e 67 2e | 20 20 46 6f 72 20 74 68 |..Wrong.| For th|
|000015d0| 65 73 65 20 74 77 6f 20 | 6e 75 6d 62 65 72 73 20 |ese two |numbers |
|000015e0| 74 6f 20 62 65 20 65 71 | 75 61 6c 2c 20 74 68 65 |to be eq|ual, the|
|000015f0| 69 72 20 72 65 61 6c 20 | 70 61 72 74 73 20 6d 75 |ir real |parts mu|
|00001600| 73 74 20 62 65 20 65 71 | 75 61 6c 20 0d 0a 00 74 |st be eq|ual ...t|
|00001610| 6f 20 65 61 63 68 20 6f | 74 68 65 72 20 61 6e 64 |o each o|ther and|
|00001620| 20 74 68 65 69 72 20 69 | 6d 61 67 69 6e 61 72 79 | their i|maginary|
|00001630| 20 70 61 72 74 73 20 6d | 75 73 74 20 62 65 20 65 | parts m|ust be e|
|00001640| 71 75 61 6c 20 74 6f 20 | 65 61 63 68 20 6f 74 68 |qual to |each oth|
|00001650| 65 72 2e 20 20 54 68 75 | 73 2c 0d 0a 00 77 65 20 |er. Thu|s,...we |
|00001660| 63 61 6e 20 73 6f 6c 76 | 65 20 74 68 65 20 70 72 |can solv|e the pr|
|00001670| 6f 62 6c 65 6d 20 61 73 | 20 66 6f 6c 6c 6f 77 73 |oblem as| follows|
|00001680| 2e 12 30 0d 0a 00 0d 0b | 00 20 20 20 20 20 11 33 |..0.....|. .3|
|00001690| 61 20 11 31 2b 20 35 20 | 3d 20 37 20 20 20 20 20 |a .1+ 5 |= 7 |
|000016a0| 61 6e 64 20 20 20 20 20 | 11 33 62 20 11 31 2d 20 |and |.3b .1- |
|000016b0| 31 20 3d 20 2d 33 0d 0a | 00 20 20 20 20 20 20 20 |1 = -3..|. |
|000016c0| 20 20 11 33 61 20 11 31 | 3d 20 32 20 20 20 20 20 | .3a .1|= 2 |
|000016d0| 20 20 20 20 20 20 20 20 | 20 20 20 20 11 33 62 20 | | .3b |
|000016e0| 11 31 3d 20 2d 32 0d 0a | 00 00 17 4f 0c 0d 0b 00 |.1= -2..|...O....|
|000016f0| 57 72 6f 6e 67 2e 20 20 | 57 65 20 70 65 72 66 6f |Wrong. |We perfo|
|00001700| 72 6d 20 74 68 65 20 69 | 6e 64 69 63 61 74 65 64 |rm the i|ndicated|
|00001710| 20 64 69 76 69 73 69 6f | 6e 20 61 73 20 66 6f 6c | divisio|n as fol|
|00001720| 6c 6f 77 73 2e 12 30 0d | 0a 00 0d 0b 00 20 20 20 |lows..0.|..... |
|00001730| 20 20 20 20 34 11 33 69 | 20 20 20 20 20 20 20 11 | 4.3i| .|
|00001740| 31 34 11 33 69 20 20 20 | 20 20 11 31 31 20 2b 20 |14.3i | .11 + |
|00001750| 33 11 33 69 0d 0b 00 20 | 20 20 20 20 11 34 32 32 |3.3i... | .422|
|00001760| 32 32 32 32 20 11 31 3d | 20 11 34 32 32 32 32 32 |2222 .1=| .422222|
|00001770| 32 20 2a 20 32 32 32 32 | 32 32 20 20 20 20 20 20 |2 * 2222|22 |
|00001780| 20 20 20 20 20 20 20 20 | 11 32 12 31 4d 75 6c 74 | |.2.1Mult|
|00001790| 69 70 6c 79 20 62 79 20 | 63 6f 6e 6a 75 67 61 74 |iply by |conjugat|
|000017a0| 65 12 30 0d 0b 00 20 20 | 20 20 20 11 31 31 20 2d |e.0... | .11 -|
|000017b0| 20 33 11 33 69 20 20 20 | 11 31 31 20 2d 20 33 11 | 3.3i |.11 - 3.|
|000017c0| 33 69 20 20 20 11 31 31 | 20 2b 20 33 11 33 69 0d |3i .11| + 3.3i.|
|000017d0| 0a 00 20 20 20 20 20 20 | 20 20 20 20 20 20 20 20 |.. | |
|000017e0| 20 20 20 11 31 34 11 33 | 69 11 31 28 31 20 2b 20 | .14.3|i.1(1 + |
|000017f0| 33 11 33 69 11 31 29 0d | 0b 00 20 20 20 20 20 20 |3.3i.1).|.. |
|00001800| 20 20 20 20 20 20 3d 20 | 11 34 32 32 32 32 32 32 | = |.4222222|
|00001810| 32 32 32 32 32 32 32 32 | 32 32 20 20 20 20 20 20 |22222222|22 |
|00001820| 20 20 20 20 20 20 20 0d | 0b 00 20 20 20 20 20 20 | .|.. |
|00001830| 20 20 20 20 20 20 20 20 | 11 31 28 31 20 2d 20 33 | |.1(1 - 3|
|00001840| 11 33 69 11 31 29 28 31 | 20 2b 20 33 11 33 69 11 |.3i.1)(1| + 3.3i.|
|00001850| 31 29 0d 0a 00 20 20 20 | 20 20 20 20 20 20 20 20 |1)... | |
|00001860| 20 20 20 34 11 33 69 11 | 31 28 31 20 2b 20 33 11 | 4.3i.|1(1 + 3.|
|00001870| 33 69 11 31 29 20 20 20 | 34 11 33 69 20 11 31 2d |3i.1) |4.3i .1-|
|00001880| 20 31 32 0d 0b 00 20 20 | 20 20 20 20 20 20 20 20 | 12... | |
|00001890| 20 20 3d 20 11 34 32 32 | 32 32 32 32 32 32 32 32 | = .422|22222222|
|000018a0| 20 11 31 3d 20 11 34 32 | 32 32 32 32 32 32 0d 0b | .1= .42|222222..|
|000018b0| 00 20 20 20 20 20 20 20 | 20 20 20 20 20 20 20 20 |. | |
|000018c0| 20 20 11 32 32 20 20 20 | 20 32 0d 0b 00 20 20 20 | .22 | 2... |
|000018d0| 20 20 20 20 20 20 20 20 | 20 20 20 20 20 11 31 31 | | .11|
|000018e0| 20 20 2b 20 33 20 20 20 | 20 20 20 20 20 31 30 0d | + 3 | 10.|
|000018f0| 0a 00 20 20 20 20 20 20 | 20 20 20 20 20 20 20 20 |.. | |
|00001900| 20 31 32 20 20 20 20 34 | 20 20 20 20 20 36 20 20 | 12 4| 6 |
|00001910| 20 32 0d 0b 00 20 20 20 | 20 20 20 20 20 20 20 20 | 2... | |
|00001920| 20 3d 20 2d 11 34 32 32 | 20 11 31 2b 20 11 34 32 | = -.422| .1+ .42|
|00001930| 32 11 33 69 20 11 31 3d | 20 2d 11 34 32 20 11 31 |2.3i .1=| -.42 .1|
|00001940| 2b 20 11 34 32 11 33 69 | 20 20 20 20 20 20 20 20 |+ .42.3i| |
|00001950| 20 20 11 32 12 31 53 74 | 61 6e 64 61 72 64 20 66 | .2.1St|andard f|
|00001960| 6f 72 6d 12 30 0d 0b 00 | 20 20 20 20 20 20 20 20 |orm.0...| |
|00001970| 20 20 20 20 20 20 20 11 | 31 31 30 20 20 20 31 30 | .|110 10|
|00001980| 20 20 20 20 20 35 20 20 | 20 35 0d 0a 00 00 17 4f | 5 | 5.....O|
|00001990| 0c 0d 0b 00 57 72 6f 6e | 67 2e 20 20 57 65 20 70 |....Wron|g. We p|
|000019a0| 65 72 66 6f 72 6d 20 74 | 68 65 20 69 6e 64 69 63 |erform t|he indic|
|000019b0| 61 74 65 64 20 64 69 76 | 69 73 69 6f 6e 20 61 73 |ated div|ision as|
|000019c0| 20 66 6f 6c 6c 6f 77 73 | 2e 12 30 0d 0a 00 0d 0b | follows|..0.....|
|000019d0| 00 20 20 20 20 20 20 20 | 34 11 33 69 20 20 20 20 |. |4.3i |
|000019e0| 20 20 20 11 31 34 11 33 | 69 20 20 20 20 20 11 31 | .14.3|i .1|
|000019f0| 31 20 2b 20 33 11 33 69 | 0d 0b 00 20 20 20 20 20 |1 + 3.3i|... |
|00001a00| 11 34 32 32 32 32 32 32 | 20 11 31 3d 20 11 34 32 |.4222222| .1= .42|
|00001a10| 32 32 32 32 32 20 2a 20 | 32 32 32 32 32 32 20 20 |22222 * |222222 |
|00001a20| 20 20 20 20 20 20 20 20 | 20 20 20 20 11 32 12 31 | | .2.1|
|00001a30| 4d 75 6c 74 69 70 6c 79 | 20 62 79 20 63 6f 6e 6a |Multiply| by conj|
|00001a40| 75 67 61 74 65 12 30 0d | 0b 00 20 20 20 20 20 11 |ugate.0.|.. .|
|00001a50| 31 31 20 2d 20 33 11 33 | 69 20 20 20 11 31 31 20 |11 - 3.3|i .11 |
|00001a60| 2d 20 33 11 33 69 20 20 | 20 11 31 31 20 2b 20 33 |- 3.3i | .11 + 3|
|00001a70| 11 33 69 0d 0a 00 20 20 | 20 20 20 20 20 20 20 20 |.3i... | |
|00001a80| 20 20 20 20 20 20 20 11 | 31 34 11 33 69 11 31 28 | .|14.3i.1(|
|00001a90| 31 20 2b 20 33 11 33 69 | 11 31 29 0d 0b 00 20 20 |1 + 3.3i|.1)... |
|00001aa0| 20 20 20 20 20 20 20 20 | 20 20 3d 20 11 34 32 32 | | = .422|
|00001ab0| 32 32 32 32 32 32 32 32 | 32 32 32 32 32 32 20 20 |22222222|222222 |
|00001ac0| 20 20 20 20 20 20 20 20 | 20 20 20 0d 0b 00 20 20 | | ... |
|00001ad0| 20 20 20 20 20 20 20 20 | 20 20 20 20 11 31 28 31 | | .1(1|
|00001ae0| 20 2d 20 33 11 33 69 11 | 31 29 28 31 20 2b 20 33 | - 3.3i.|1)(1 + 3|
|00001af0| 11 33 69 11 31 29 0d 0a | 00 20 20 20 20 20 20 20 |.3i.1)..|. |
|00001b00| 20 20 20 20 20 20 20 34 | 11 33 69 11 31 28 31 20 | 4|.3i.1(1 |
|00001b10| 2b 20 33 11 33 69 11 31 | 29 20 20 20 34 11 33 69 |+ 3.3i.1|) 4.3i|
|00001b20| 20 11 31 2d 20 31 32 0d | 0b 00 20 20 20 20 20 20 | .1- 12.|.. |
|00001b30| 20 20 20 20 20 20 3d 20 | 11 34 32 32 32 32 32 32 | = |.4222222|
|00001b40| 32 32 32 32 20 11 31 3d | 20 11 34 32 32 32 32 32 |2222 .1=| .422222|
|00001b50| 32 32 0d 0b 00 20 20 20 | 20 20 20 20 20 20 20 20 |22... | |
|00001b60| 20 20 20 20 20 20 11 32 | 32 20 20 20 20 32 0d 0b | .2|2 2..|
|00001b70| 00 20 20 20 20 20 20 20 | 20 20 20 20 20 20 20 20 |. | |
|00001b80| 20 11 31 31 20 20 2b 20 | 33 20 20 20 20 20 20 20 | .11 + |3 |
|00001b90| 20 31 30 0d 0a 00 20 20 | 20 20 20 20 20 20 20 20 | 10... | |
|00001ba0| 20 20 20 20 20 31 32 20 | 20 20 20 34 20 20 20 20 | 12 | 4 |
|00001bb0| 20 36 20 20 20 32 0d 0b | 00 20 20 20 20 20 20 20 | 6 2..|. |
|00001bc0| 20 20 20 20 20 3d 20 2d | 11 34 32 32 20 11 31 2b | = -|.422 .1+|
|00001bd0| 20 11 34 32 32 11 33 69 | 20 11 31 3d 20 2d 11 34 | .422.3i| .1= -.4|
|00001be0| 32 20 11 31 2b 20 11 34 | 32 11 33 69 20 20 20 20 |2 .1+ .4|2.3i |
|00001bf0| 20 20 20 20 20 20 11 32 | 12 31 53 74 61 6e 64 61 | .2|.1Standa|
|00001c00| 72 64 20 66 6f 72 6d 12 | 30 0d 0b 00 20 20 20 20 |rd form.|0... |
|00001c10| 20 20 20 20 20 20 20 20 | 20 20 20 11 31 31 30 20 | | .110 |
|00001c20| 20 20 31 30 20 20 20 20 | 20 35 20 20 20 35 0d 0a | 10 | 5 5..|
|00001c30| 00 00 17 4f 04 0d 0b 00 | 20 20 20 20 20 20 20 20 |...O....| |
|00001c40| 20 20 20 20 20 20 20 20 | 20 20 20 20 20 20 20 20 | | |
|00001c50| 20 20 20 20 20 20 20 20 | 20 20 20 36 20 20 20 32 | | 6 2|
|00001c60| 0d 0b 00 52 69 67 68 74 | 2e 20 20 41 66 74 65 72 |...Right|. After|
|00001c70| 20 64 69 76 69 64 69 6e | 67 2c 20 77 65 20 6f 62 | dividin|g, we ob|
|00001c80| 74 61 69 6e 20 2d 11 34 | 32 20 11 31 2b 20 11 34 |tain -.4|2 .1+ .4|
|00001c90| 32 11 33 69 11 31 2e 0d | 0b 00 20 20 20 20 20 20 |2.3i.1..|.. |
|00001ca0| 20 20 20 20 20 20 20 20 | 20 20 20 20 20 20 20 20 | | |
|00001cb0| 20 20 20 20 20 20 20 20 | 20 20 20 20 20 35 20 20 | | 5 |
|00001cc0| 20 35 0d 0a 00 00 17 4f | 0c 0d 0b 00 57 72 6f 6e | 5.....O|....Wron|
|00001cd0| 67 2e 20 20 57 65 20 70 | 65 72 66 6f 72 6d 20 74 |g. We p|erform t|
|00001ce0| 68 65 20 69 6e 64 69 63 | 61 74 65 64 20 64 69 76 |he indic|ated div|
|00001cf0| 69 73 69 6f 6e 20 61 73 | 20 66 6f 6c 6c 6f 77 73 |ision as| follows|
|00001d00| 2e 12 30 0d 0a 00 0d 0b | 00 20 20 20 20 20 20 20 |..0.....|. |
|00001d10| 34 11 33 69 20 20 20 20 | 20 20 20 11 31 34 11 33 |4.3i | .14.3|
|00001d20| 69 20 20 20 20 20 11 31 | 31 20 2b 20 33 11 33 69 |i .1|1 + 3.3i|
|00001d30| 0d 0b 00 20 20 20 20 20 | 11 34 32 32 32 32 32 32 |... |.4222222|
|00001d40| 20 11 31 3d 20 11 34 32 | 32 32 32 32 32 20 2a 20 | .1= .42|22222 * |
|00001d50| 32 32 32 32 32 32 20 20 | 20 20 20 20 20 20 20 20 |222222 | |
|00001d60| 20 20 20 20 11 32 12 31 | 4d 75 6c 74 69 70 6c 79 | .2.1|Multiply|
|00001d70| 20 62 79 20 63 6f 6e 6a | 75 67 61 74 65 12 30 0d | by conj|ugate.0.|
|00001d80| 0b 00 20 20 20 20 20 11 | 31 31 20 2d 20 33 11 33 |.. .|11 - 3.3|
|00001d90| 69 20 20 20 11 31 31 20 | 2d 20 33 11 33 69 20 20 |i .11 |- 3.3i |
|00001da0| 20 11 31 31 20 2b 20 33 | 11 33 69 0d 0a 00 20 20 | .11 + 3|.3i... |
|00001db0| 20 20 20 20 20 20 20 20 | 20 20 20 20 20 20 20 11 | | .|
|00001dc0| 31 34 11 33 69 11 31 28 | 31 20 2b 20 33 11 33 69 |14.3i.1(|1 + 3.3i|
|00001dd0| 11 31 29 0d 0b 00 20 20 | 20 20 20 20 20 20 20 20 |.1)... | |
|00001de0| 20 20 3d 20 11 34 32 32 | 32 32 32 32 32 32 32 32 | = .422|22222222|
|00001df0| 32 32 32 32 32 32 20 20 | 20 20 20 20 20 20 20 20 |222222 | |
|00001e00| 20 20 20 0d 0b 00 20 20 | 20 20 20 20 20 20 20 20 | ... | |
|00001e10| 20 20 20 20 11 31 28 31 | 20 2d 20 33 11 33 69 11 | .1(1| - 3.3i.|
|00001e20| 31 29 28 31 20 2b 20 33 | 11 33 69 11 31 29 0d 0a |1)(1 + 3|.3i.1)..|
|00001e30| 00 20 20 20 20 20 20 20 | 20 20 20 20 20 20 20 34 |. | 4|
|00001e40| 11 33 69 11 31 28 31 20 | 2b 20 33 11 33 69 11 31 |.3i.1(1 |+ 3.3i.1|
|00001e50| 29 20 20 20 34 11 33 69 | 20 11 31 2d 20 31 32 0d |) 4.3i| .1- 12.|
|00001e60| 0b 00 20 20 20 20 20 20 | 20 20 20 20 20 20 3d 20 |.. | = |
|00001e70| 11 34 32 32 32 32 32 32 | 32 32 32 32 20 11 31 3d |.4222222|2222 .1=|
|00001e80| 20 11 34 32 32 32 32 32 | 32 32 0d 0b 00 20 20 20 | .422222|22... |
|00001e90| 20 20 20 20 20 20 20 20 | 20 20 20 20 20 20 11 32 | | .2|
|00001ea0| 32 20 20 20 20 32 0d 0b | 00 20 20 20 20 20 20 20 |2 2..|. |
|00001eb0| 20 20 20 20 20 20 20 20 | 20 11 31 31 20 20 2b 20 | | .11 + |
|00001ec0| 33 20 20 20 20 20 20 20 | 20 31 30 0d 0a 00 20 20 |3 | 10... |
|00001ed0| 20 20 20 20 20 20 20 20 | 20 20 20 20 20 31 32 20 | | 12 |
|00001ee0| 20 20 20 34 20 20 20 20 | 20 36 20 20 20 32 0d 0b | 4 | 6 2..|
|00001ef0| 00 20 20 20 20 20 20 20 | 20 20 20 20 20 3d 20 2d |. | = -|
|00001f00| 11 34 32 32 20 11 31 2b | 20 11 34 32 32 11 33 69 |.422 .1+| .422.3i|
|00001f10| 20 11 31 3d 20 2d 11 34 | 32 20 11 31 2b 20 11 34 | .1= -.4|2 .1+ .4|
|00001f20| 32 11 33 69 20 20 20 20 | 20 20 20 20 20 20 11 32 |2.3i | .2|
|00001f30| 12 31 53 74 61 6e 64 61 | 72 64 20 66 6f 72 6d 12 |.1Standa|rd form.|
|00001f40| 30 0d 0b 00 20 20 20 20 | 20 20 20 20 20 20 20 20 |0... | |
|00001f50| 20 20 20 11 31 31 30 20 | 20 20 31 30 20 20 20 20 | .110 | 10 |
|00001f60| 20 35 20 20 20 35 0d 0a | 00 00 17 4f 09 0d 0b 00 | 5 5..|...O....|
|00001f70| 57 72 6f 6e 67 2e 20 20 | 57 65 20 64 69 76 69 64 |Wrong. |We divid|
|00001f80| 65 20 61 73 20 66 6f 6c | 6c 6f 77 73 2e 12 30 0d |e as fol|lows..0.|
|00001f90| 0a 00 0d 0b 00 20 20 20 | 20 20 32 20 2b 20 33 11 |..... | 2 + 3.|
|00001fa0| 33 69 20 20 20 11 31 32 | 20 2b 20 33 11 33 69 20 |3i .12| + 3.3i |
|00001fb0| 20 20 11 31 31 20 2d 20 | 32 11 33 69 0d 0b 00 20 | .11 - |2.3i... |
|00001fc0| 20 20 20 20 11 34 32 32 | 32 32 32 32 20 11 31 3d | .422|2222 .1=|
|00001fd0| 20 11 34 32 32 32 32 32 | 32 20 2a 20 32 32 32 32 | .422222|2 * 2222|
|00001fe0| 32 32 20 20 20 20 20 20 | 20 20 20 20 20 20 20 20 |22 | |
|00001ff0| 20 20 20 20 20 20 20 11 | 32 12 31 4d 75 6c 74 69 | .|2.1Multi|
|00002000| 70 6c 79 20 62 79 20 63 | 6f 6e 6a 75 67 61 74 65 |ply by c|onjugate|
|00002010| 12 30 0d 0b 00 20 20 20 | 20 20 11 31 31 20 2b 20 |.0... | .11 + |
|00002020| 32 11 33 69 20 20 20 11 | 31 31 20 2b 20 32 11 33 |2.3i .|11 + 2.3|
|00002030| 69 20 20 20 11 31 31 20 | 2d 20 32 11 33 69 0d 0a |i .11 |- 2.3i..|
|00002040| 00 20 20 20 20 20 20 20 | 20 20 20 20 20 20 20 20 |. | |
|00002050| 20 20 20 20 20 20 20 20 | 20 11 32 32 0d 0b 00 20 | | .22... |
|00002060| 20 20 20 20 20 20 20 20 | 20 20 20 20 20 11 31 32 | | .12|
|00002070| 20 2d 20 11 33 69 20 11 | 31 2d 20 36 11 33 69 20 | - .3i .|1- 6.3i |
|00002080| 20 20 20 11 31 32 20 2d | 20 11 33 69 20 11 31 2d | .12 -| .3i .1-|
|00002090| 20 36 28 2d 31 29 0d 0b | 00 20 20 20 20 20 20 20 | 6(-1)..|. |
|000020a0| 20 20 20 20 20 3d 20 11 | 34 32 32 32 32 32 32 32 | = .|42222222|
|000020b0| 32 32 32 32 20 11 31 3d | 20 11 34 32 32 32 32 32 |2222 .1=| .422222|
|000020c0| 32 32 32 32 32 32 32 32 | 0d 0b 00 20 20 20 20 20 |22222222|... |
|000020d0| 20 20 20 20 20 20 20 20 | 20 20 20 20 11 32 32 20 | | .22 |
|000020e0| 20 20 20 32 0d 0b 00 20 | 20 20 20 20 20 20 20 20 | 2... | |
|000020f0| 20 20 20 20 20 20 20 11 | 31 31 20 20 2b 20 32 20 | .|11 + 2 |
|00002100| 20 20 20 20 20 20 20 20 | 20 20 20 35 0d 0a 00 20 | | 5... |
|00002110| 20 20 20 20 20 20 20 20 | 20 20 20 20 20 38 20 2d | | 8 -|
|00002120| 20 11 33 69 20 20 20 11 | 31 38 20 20 20 31 0d 0b | .3i .|18 1..|
|00002130| 00 20 20 20 20 20 20 20 | 20 20 20 20 20 3d 20 11 |. | = .|
|00002140| 34 32 32 32 32 32 20 11 | 31 3d 20 11 34 32 20 11 |422222 .|1= .42 .|
|00002150| 31 2d 20 11 34 32 11 33 | 69 20 20 20 20 20 20 20 |1- .42.3|i |
|00002160| 20 20 20 20 20 20 20 20 | 20 20 20 20 20 20 20 11 | | .|
|00002170| 32 12 31 53 74 61 6e 64 | 61 72 64 20 66 6f 72 6d |2.1Stand|ard form|
|00002180| 12 30 0d 0b 00 20 20 20 | 20 20 20 20 20 20 20 20 |.0... | |
|00002190| 20 20 20 20 20 11 31 35 | 20 20 20 20 20 35 20 20 | .15| 5 |
|000021a0| 20 35 0d 0a 00 00 17 4f | 09 0d 0b 00 57 72 6f 6e | 5.....O|....Wron|
|000021b0| 67 2e 20 20 57 65 20 64 | 69 76 69 64 65 20 61 73 |g. We d|ivide as|
|000021c0| 20 66 6f 6c 6c 6f 77 73 | 2e 12 30 0d 0a 00 0d 0b | follows|..0.....|
|000021d0| 00 20 20 20 20 20 32 20 | 2b 20 33 11 33 69 20 20 |. 2 |+ 3.3i |
|000021e0| 20 11 31 32 20 2b 20 33 | 11 33 69 20 20 20 11 31 | .12 + 3|.3i .1|
|000021f0| 31 20 2d 20 32 11 33 69 | 0d 0b 00 20 20 20 20 20 |1 - 2.3i|... |
|00002200| 11 34 32 32 32 32 32 32 | 20 11 31 3d 20 11 34 32 |.4222222| .1= .42|
|00002210| 32 32 32 32 32 20 2a 20 | 32 32 32 32 32 32 20 20 |22222 * |222222 |
|00002220| 20 20 20 20 20 20 20 20 | 20 20 20 20 20 20 20 20 | | |
|00002230| 20 20 20 11 32 12 31 4d | 75 6c 74 69 70 6c 79 20 | .2.1M|ultiply |
|00002240| 62 79 20 63 6f 6e 6a 75 | 67 61 74 65 12 30 0d 0b |by conju|gate.0..|
|00002250| 00 20 20 20 20 20 11 31 | 31 20 2b 20 32 11 33 69 |. .1|1 + 2.3i|
|00002260| 20 20 20 11 31 31 20 2b | 20 32 11 33 69 20 20 20 | .11 +| 2.3i |
|00002270| 11 31 31 20 2d 20 32 11 | 33 69 0d 0a 00 20 20 20 |.11 - 2.|3i... |
|00002280| 20 20 20 20 20 20 20 20 | 20 20 20 20 20 20 20 20 | | |
|00002290| 20 20 20 20 20 11 32 32 | 0d 0b 00 20 20 20 20 20 | .22|... |
|000022a0| 20 20 20 20 20 20 20 20 | 20 11 31 32 20 2d 20 11 | | .12 - .|
|000022b0| 33 69 20 11 31 2d 20 36 | 11 33 69 20 20 20 20 11 |3i .1- 6|.3i .|
|000022c0| 31 32 20 2d 20 11 33 69 | 20 11 31 2d 20 36 28 2d |12 - .3i| .1- 6(-|
|000022d0| 31 29 0d 0b 00 20 20 20 | 20 20 20 20 20 20 20 20 |1)... | |
|000022e0| 20 3d 20 11 34 32 32 32 | 32 32 32 32 32 32 32 32 | = .4222|22222222|
|000022f0| 20 11 31 3d 20 11 34 32 | 32 32 32 32 32 32 32 32 | .1= .42|22222222|
|00002300| 32 32 32 32 0d 0b 00 20 | 20 20 20 20 20 20 20 20 |2222... | |
|00002310| 20 20 20 20 20 20 20 20 | 11 32 32 20 20 20 20 32 | |.22 2|
|00002320| 0d 0b 00 20 20 20 20 20 | 20 20 20 20 20 20 20 20 |... | |
|00002330| 20 20 20 11 31 31 20 20 | 2b 20 32 20 20 20 20 20 | .11 |+ 2 |
|00002340| 20 20 20 20 20 20 20 35 | 0d 0a 00 20 20 20 20 20 | 5|... |
|00002350| 20 20 20 20 20 20 20 20 | 20 38 20 2d 20 11 33 69 | | 8 - .3i|
|00002360| 20 20 20 11 31 38 20 20 | 20 31 0d 0b 00 20 20 20 | .18 | 1... |
|00002370| 20 20 20 20 20 20 20 20 | 20 3d 20 11 34 32 32 32 | | = .4222|
|00002380| 32 32 20 11 31 3d 20 11 | 34 32 20 11 31 2d 20 11 |22 .1= .|42 .1- .|
|00002390| 34 32 11 33 69 20 20 20 | 20 20 20 20 20 20 20 20 |42.3i | |
|000023a0| 20 20 20 20 20 20 20 20 | 20 20 20 11 32 12 31 53 | | .2.1S|
|000023b0| 74 61 6e 64 61 72 64 20 | 66 6f 72 6d 12 30 0d 0b |tandard |form.0..|
|000023c0| 00 20 20 20 20 20 20 20 | 20 20 20 20 20 20 20 20 |. | |
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|000023f0| 57 65 20 64 69 76 69 64 | 65 20 61 73 20 66 6f 6c |We divid|e as fol|
|00002400| 6c 6f 77 73 2e 12 30 0d | 0a 00 0d 0b 00 20 20 20 |lows..0.|..... |
|00002410| 20 20 32 20 2b 20 33 11 | 33 69 20 20 20 11 31 32 | 2 + 3.|3i .12|
|00002420| 20 2b 20 33 11 33 69 20 | 20 20 11 31 31 20 2d 20 | + 3.3i | .11 - |
|00002430| 32 11 33 69 0d 0b 00 20 | 20 20 20 20 11 34 32 32 |2.3i... | .422|
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|00002450| 32 20 2a 20 32 32 32 32 | 32 32 20 20 20 20 20 20 |2 * 2222|22 |
|00002460| 20 20 20 20 20 20 20 20 | 20 20 20 20 20 20 20 11 | | .|
|00002470| 32 12 31 4d 75 6c 74 69 | 70 6c 79 20 62 79 20 63 |2.1Multi|ply by c|
|00002480| 6f 6e 6a 75 67 61 74 65 | 12 30 0d 0b 00 20 20 20 |onjugate|.0... |
|00002490| 20 20 11 31 31 20 2b 20 | 32 11 33 69 20 20 20 11 | .11 + |2.3i .|
|000024a0| 31 31 20 2b 20 32 11 33 | 69 20 20 20 11 31 31 20 |11 + 2.3|i .11 |
|000024b0| 2d 20 32 11 33 69 0d 0a | 00 20 20 20 20 20 20 20 |- 2.3i..|. |
|000024c0| 20 20 20 20 20 20 20 20 | 20 20 20 20 20 20 20 20 | | |
|000024d0| 20 11 32 32 0d 0b 00 20 | 20 20 20 20 20 20 20 20 | .22... | |
|000024e0| 20 20 20 20 20 11 31 32 | 20 2d 20 11 33 69 20 11 | .12| - .3i .|
|000024f0| 31 2d 20 36 11 33 69 20 | 20 20 20 11 31 32 20 2d |1- 6.3i | .12 -|
|00002500| 20 11 33 69 20 11 31 2d | 20 36 28 2d 31 29 0d 0b | .3i .1-| 6(-1)..|
|00002510| 00 20 20 20 20 20 20 20 | 20 20 20 20 20 3d 20 11 |. | = .|
|00002520| 34 32 32 32 32 32 32 32 | 32 32 32 32 20 11 31 3d |42222222|2222 .1=|
|00002530| 20 11 34 32 32 32 32 32 | 32 32 32 32 32 32 32 32 | .422222|22222222|
|00002540| 0d 0b 00 20 20 20 20 20 | 20 20 20 20 20 20 20 20 |... | |
|00002550| 20 20 20 20 11 32 32 20 | 20 20 20 32 0d 0b 00 20 | .22 | 2... |
|00002560| 20 20 20 20 20 20 20 20 | 20 20 20 20 20 20 20 11 | | .|
|00002570| 31 31 20 20 2b 20 32 20 | 20 20 20 20 20 20 20 20 |11 + 2 | |
|00002580| 20 20 20 35 0d 0a 00 20 | 20 20 20 20 20 20 20 20 | 5... | |
|00002590| 20 20 20 20 20 38 20 2d | 20 11 33 69 20 20 20 11 | 8 -| .3i .|
|000025a0| 31 38 20 20 20 31 0d 0b | 00 20 20 20 20 20 20 20 |18 1..|. |
|000025b0| 20 20 20 20 20 3d 20 11 | 34 32 32 32 32 32 20 11 | = .|422222 .|
|000025c0| 31 3d 20 11 34 32 20 11 | 31 2d 20 11 34 32 11 33 |1= .42 .|1- .42.3|
|000025d0| 69 20 20 20 20 20 20 20 | 20 20 20 20 20 20 20 20 |i | |
|000025e0| 20 20 20 20 20 20 20 11 | 32 12 31 53 74 61 6e 64 | .|2.1Stand|
|000025f0| 61 72 64 20 66 6f 72 6d | 12 30 0d 0b 00 20 20 20 |ard form|.0... |
|00002600| 20 20 20 20 20 20 20 20 | 20 20 20 20 20 11 31 35 | | .15|
|00002610| 20 20 20 20 20 35 20 20 | 20 35 0d 0a 00 00 17 4f | 5 | 5.....O|
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|00002640| 20 20 20 20 20 20 38 20 | 20 20 31 0d 0b 00 52 69 | 8 | 1...Ri|
|00002650| 67 68 74 2e 20 20 41 66 | 74 65 72 20 64 69 76 69 |ght. Af|ter divi|
|00002660| 64 69 6e 67 2c 20 77 65 | 20 6f 62 74 61 69 6e 20 |ding, we| obtain |
|00002670| 11 34 32 20 11 31 2d 20 | 11 34 32 11 33 69 11 31 |.42 .1- |.42.3i.1|
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|000026a0| 20 20 20 20 20 20 35 20 | 20 20 35 0d 0a 00 00 17 | 5 | 5.....|
|000026b0| 4f 0a 0d 0b 00 57 72 6f | 6e 67 2e 20 20 55 73 69 |O....Wro|ng. Usi|
|000026c0| 6e 67 20 74 68 65 20 51 | 75 61 64 72 61 74 69 63 |ng the Q|uadratic|
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|000026e0| 61 20 11 31 3d 20 31 2c | 20 11 33 62 20 11 31 3d |a .1= 1,| .3b .1=|
|000026f0| 20 33 20 61 6e 64 20 11 | 33 63 20 11 31 3d 20 33 | 3 and .|3c .1= 3|
|00002700| 2c 20 77 65 20 73 6f 6c | 76 65 0d 0a 00 61 73 20 |, we sol|ve...as |
|00002710| 66 6f 6c 6c 6f 77 73 2e | 12 30 0d 0b 00 20 20 20 |follows.|.0... |
|00002720| 20 20 20 20 20 20 20 20 | 20 20 20 20 11 34 67 32 | | .4g2|
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|00002770| 20 2d 20 34 28 31 29 28 | 33 29 20 20 20 20 20 20 | - 4(1)(|3) |
|00002780| 20 20 20 20 20 20 20 20 | 20 20 20 20 20 20 20 20 | | |
|00002790| 20 11 32 12 31 53 75 62 | 73 74 69 74 75 74 65 20 | .2.1Sub|stitute |
|000027a0| 69 6e 74 6f 12 30 0d 0b | 00 20 20 20 20 11 33 78 |into.0..|. .3x|
|000027b0| 20 11 31 3d 20 11 34 32 | 32 32 32 32 32 32 32 32 | .1= .42|22222222|
|000027c0| 32 32 32 32 32 32 32 32 | 32 32 32 32 20 20 20 20 |22222222|2222 |
|000027d0| 20 20 20 20 20 20 20 20 | 20 20 20 20 20 20 20 20 | | |
|000027e0| 20 20 20 0d 0b 00 20 20 | 20 20 20 20 20 20 20 20 | ... | |
|000027f0| 20 20 20 20 20 20 20 11 | 31 32 28 31 29 20 20 20 | .|12(1) |
|00002800| 20 20 20 20 20 20 20 20 | 20 20 20 20 20 20 20 20 | | |
|00002810| 20 20 20 20 20 20 20 20 | 20 20 20 20 11 32 12 31 | | .2.1|
|00002820| 51 75 61 64 72 61 74 69 | 63 20 46 6f 72 6d 75 6c |Quadrati|c Formul|
|00002830| 61 12 30 0d 0a 00 20 20 | 20 20 20 20 20 20 20 20 |a.0... | |
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|00002860| 20 20 44 32 0d 0b 00 20 | 20 20 20 20 20 20 20 11 | D2... | .|
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|000028c0| 20 11 31 3d 20 11 34 32 | 32 32 32 32 32 32 32 32 | .1= .42|22222222|
|000028d0| 20 11 31 3d 20 2d 11 34 | 32 20 2b 20 32 32 32 32 | .1= -.4|2 + 2222|
|000028e0| 20 20 20 20 20 20 20 11 | 32 12 31 53 6f 6c 75 74 | .|2.1Solut|
|000028f0| 69 6f 6e 73 12 30 0d 0b | 00 20 20 20 20 20 20 20 |ions.0..|. |
|00002900| 20 20 20 20 20 20 20 11 | 31 32 20 20 20 20 20 20 | .|12 |
|00002910| 20 20 20 20 20 20 20 32 | 20 20 20 20 20 20 20 20 | 2| |
|00002920| 32 20 20 20 20 20 32 0d | 0a 00 00 17 4f 06 20 20 |2 2.|....O. |
|00002930| 20 20 20 20 20 20 20 20 | 20 20 20 20 20 20 20 20 | | |
|00002940| 20 20 20 20 20 20 20 20 | 20 20 20 20 20 20 20 20 | | |
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|00002960| 20 20 20 20 20 20 20 20 | 20 20 11 34 44 32 0d 0b | | .4D2..|
|00002970| 00 20 20 20 20 20 20 20 | 20 20 20 20 20 20 20 20 |. | |
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|00002990| 20 20 20 20 20 20 20 20 | 20 20 20 20 20 20 20 20 | | |
|000029a0| 20 20 20 20 20 20 20 20 | 11 31 33 20 20 20 11 34 | |.13 .4|
|000029b0| 53 20 11 31 33 11 33 69 | 0d 0b 00 11 31 52 69 67 |S .13.3i|....1Rig|
|000029c0| 68 74 2e 20 20 54 68 65 | 20 67 69 76 65 6e 20 65 |ht. The| given e|
|000029d0| 71 75 61 74 69 6f 6e 20 | 68 61 73 20 74 77 6f 20 |quation |has two |
|000029e0| 63 6f 6d 70 6c 65 78 20 | 73 6f 6c 75 74 69 6f 6e |complex |solution|
|000029f0| 73 3a 20 2d 11 34 32 20 | 11 31 2b 20 11 34 32 32 |s: -.42 |.1+ .422|
|00002a00| 32 32 20 11 31 61 6e 64 | 20 0d 0b 00 20 20 20 20 |22 .1and| ... |
|00002a10| 20 20 20 20 20 20 20 20 | 20 20 20 20 20 20 20 20 | | |
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|00002a50| 20 20 20 11 34 44 32 0d | 0b 00 20 11 31 33 20 20 | .4D2.|.. .13 |
|00002a60| 20 11 34 53 20 11 31 33 | 11 33 69 0d 0b 00 11 31 | .4S .13|.3i....1|
|00002a70| 2d 11 34 32 20 11 31 2d | 20 11 34 32 32 32 32 20 |-.42 .1-| .42222 |
|00002a80| 11 31 2e 0d 0b 00 20 32 | 20 20 20 20 20 32 0d 0a |.1.... 2| 2..|
|00002a90| 00 00 17 4f 0a 0d 0b 00 | 57 72 6f 6e 67 2e 20 20 |...O....|Wrong. |
|00002aa0| 55 73 69 6e 67 20 74 68 | 65 20 51 75 61 64 72 61 |Using th|e Quadra|
|00002ab0| 74 69 63 20 46 6f 72 6d | 75 6c 61 20 77 69 74 68 |tic Form|ula with|
|00002ac0| 20 11 33 61 20 11 31 3d | 20 31 2c 20 11 33 62 20 | .3a .1=| 1, .3b |
|00002ad0| 11 31 3d 20 33 20 61 6e | 64 20 11 33 63 20 11 31 |.1= 3 an|d .3c .1|
|00002ae0| 3d 20 33 2c 20 77 65 20 | 73 6f 6c 76 65 0d 0a 00 |= 3, we |solve...|
|00002af0| 61 73 20 66 6f 6c 6c 6f | 77 73 2e 12 30 0d 0b 00 |as follo|ws..0...|
|00002b00| 20 20 20 20 20 20 20 20 | 20 20 20 20 20 20 20 11 | | .|
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|00003d70| 20 41 66 74 65 72 20 6d | 75 6c 74 69 70 6c 79 69 | After m|ultiplyi|
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|000054b0| 35 20 20 43 6f 6d 70 6c | 65 78 20 4e 75 6d 62 65 |5 Compl|ex Numbe|
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|00005500| 20 20 20 20 20 20 20 20 | 44 32 32 0d 0b 00 20 11 | |D22... .|
|00005510| 31 37 2e 20 20 46 69 6e | 64 20 74 68 65 20 63 6f |17. Fin|d the co|
|00005520| 6e 6a 75 67 61 74 65 20 | 6f 66 20 31 20 2b 20 11 |njugate |of 1 + .|
|00005530| 34 53 20 11 31 2d 33 2e | 20 20 54 68 65 6e 20 66 |4S .1-3.| Then f|
|00005540| 69 6e 64 20 74 68 65 20 | 70 72 6f 64 75 63 74 20 |ind the |product |
|00005550| 6f 66 20 31 20 2b 20 11 | 34 53 20 11 31 2d 33 20 |of 1 + .|4S .1-3 |
|00005560| 61 6e 64 20 0d 0a 00 20 | 20 20 20 20 69 74 73 20 |and ... | its |
|00005570| 63 6f 6e 6a 75 67 61 74 | 65 2e 0d 0a 00 0d 0a 00 |conjugat|e.......|
|00005580| 20 20 20 20 20 20 20 20 | 20 20 20 20 20 20 20 20 | | |
|00005590| 20 20 20 20 20 20 20 20 | 20 11 34 44 32 20 20 20 | | .4D2 |
|000055a0| 20 20 20 20 20 20 20 20 | 20 20 20 20 20 20 20 20 | | |
|000055b0| 20 20 20 20 20 20 20 20 | 20 20 20 20 44 32 0d 0b | | D2..|
|000055c0| 00 20 20 20 20 20 11 31 | 0e 32 2d 35 2d 32 39 61 |. .1|.2-5-29a|
|000055d0| 0e 28 61 29 0f 20 43 6f | 6e 6a 75 67 61 74 65 3a |.(a). Co|njugate:|
|000055e0| 20 31 20 2d 20 11 34 53 | 20 11 31 33 20 20 20 20 | 1 - .4S| .13 |
|000055f0| 20 20 20 20 20 20 20 0e | 32 2d 35 2d 32 39 62 0e | .|2-5-29b.|
|00005600| 28 62 29 0f 20 43 6f 6e | 6a 75 67 61 74 65 3a 20 |(b). Con|jugate: |
|00005610| 31 20 2d 20 11 34 53 20 | 11 31 33 11 33 69 0d 0a |1 - .4S |.13.3i..|
|00005620| 00 20 20 20 20 20 20 20 | 20 20 11 31 50 72 6f 64 |. | .1Prod|
|00005630| 75 63 74 3a 20 31 20 2d | 20 33 11 33 69 20 20 20 |uct: 1 -| 3.3i |
|00005640| 20 20 20 20 20 20 20 20 | 20 20 20 20 20 20 20 11 | | .|
|00005650| 31 50 72 6f 64 75 63 74 | 3a 20 2d 33 0d 0a 00 0d |1Product|: -3....|
|00005660| 0b 00 20 20 20 20 20 20 | 20 20 20 20 20 20 20 20 |.. | |
|00005670| 20 20 20 20 20 20 20 20 | 20 20 20 11 34 44 32 20 | | .4D2 |
|00005680| 20 20 20 20 20 20 20 20 | 20 20 20 20 20 20 20 20 | | |
|00005690| 20 20 20 20 20 20 20 20 | 20 20 20 20 20 20 44 32 | | D2|
|000056a0| 0d 0b 00 20 20 20 20 20 | 11 31 0e 32 2d 35 2d 32 |... |.1.2-5-2|
|000056b0| 39 63 0e 28 63 29 0f 20 | 43 6f 6e 6a 75 67 61 74 |9c.(c). |Conjugat|
|000056c0| 65 3a 20 31 20 2b 20 11 | 34 53 20 11 31 33 20 20 |e: 1 + .|4S .13 |
|000056d0| 20 20 20 20 20 20 20 20 | 20 0e 32 2d 35 2d 32 39 | | .2-5-29|
|000056e0| 64 0e 28 64 29 0f 20 43 | 6f 6e 6a 75 67 61 74 65 |d.(d). C|onjugate|
|000056f0| 3a 20 31 20 2d 20 11 34 | 53 20 11 31 33 11 33 69 |: 1 - .4|S .13.3i|
|00005700| 0d 0a 00 20 20 20 20 20 | 20 20 20 20 11 31 50 72 |... | .1Pr|
|00005710| 6f 64 75 63 74 3a 20 31 | 20 2b 20 33 11 33 69 20 |oduct: 1| + 3.3i |
|00005720| 20 20 20 20 20 20 20 20 | 20 20 20 20 20 20 20 20 | | |
|00005730| 20 11 31 50 72 6f 64 75 | 63 74 3a 20 34 0d 0a 00 | .1Produ|ct: 4...|
|00005740| 0d 0a 00 59 6f 75 20 6d | 61 79 20 77 61 6e 74 20 |...You m|ay want |
|00005750| 74 6f 20 72 65 76 69 65 | 77 20 10 31 2d 35 2d 32 |to revie|w .1-5-2|
|00005760| 0e 65 31 2d 35 2d 37 0e | 47 75 69 64 65 64 20 45 |.e1-5-7.|Guided E|
|00005770| 78 61 6d 70 6c 65 20 37 | 2e 0f 0d 0a 00 53 65 63 |xample 7|.....Sec|
|00005780| 74 69 6f 6e 20 31 2e 35 | 20 20 43 6f 6d 70 6c 65 |tion 1.5| Comple|
|00005790| 78 20 4e 75 6d 62 65 72 | 73 0d 0b 00 20 38 2e 20 |x Number|s... 8. |
|000057a0| 20 46 69 6e 64 20 74 68 | 65 20 63 6f 6e 6a 75 67 | Find th|e conjug|
|000057b0| 61 74 65 20 6f 66 20 31 | 30 11 33 69 11 31 2e 20 |ate of 1|0.3i.1. |
|000057c0| 20 54 68 65 6e 20 66 69 | 6e 64 20 74 68 65 20 70 | Then fi|nd the p|
|000057d0| 72 6f 64 75 63 74 20 6f | 66 20 31 30 11 33 69 20 |roduct o|f 10.3i |
|000057e0| 11 31 61 6e 64 20 69 74 | 73 20 0d 0a 00 20 20 20 |.1and it|s ... |
|000057f0| 20 20 63 6f 6e 6a 75 67 | 61 74 65 2e 0d 0a 00 0d | conjug|ate.....|
|00005800| 0a 00 20 20 20 20 20 0e | 32 2d 35 2d 33 31 61 0e |.. .|2-5-31a.|
|00005810| 28 61 29 0f 20 43 6f 6e | 6a 75 67 61 74 65 3a 20 |(a). Con|jugate: |
|00005820| 2d 11 33 69 20 20 20 20 | 20 20 20 20 20 20 20 20 |-.3i | |
|00005830| 20 20 20 20 11 31 0e 32 | 2d 35 2d 33 31 62 0e 28 | .1.2|-5-31b.(|
|00005840| 62 29 0f 20 43 6f 6e 6a | 75 67 61 74 65 3a 20 31 |b). Conj|ugate: 1|
|00005850| 30 11 33 69 0d 0a 00 20 | 20 20 20 20 20 20 20 20 |0.3i... | |
|00005860| 11 31 50 72 6f 64 75 63 | 74 3a 20 2d 31 30 20 20 |.1Produc|t: -10 |
|00005870| 20 20 20 20 20 20 20 20 | 20 20 20 20 20 20 20 20 | | |
|00005880| 20 20 20 50 72 6f 64 75 | 63 74 3a 20 2d 31 30 30 | Produ|ct: -100|
|00005890| 0d 0a 00 0d 0b 00 20 20 | 20 20 20 0e 32 2d 35 2d |...... | .2-5-|
|000058a0| 33 31 63 0e 28 63 29 0f | 20 43 6f 6e 6a 75 67 61 |31c.(c).| Conjuga|
|000058b0| 74 65 3a 20 2d 31 30 11 | 33 69 20 20 20 20 20 20 |te: -10.|3i |
|000058c0| 20 20 20 20 20 20 20 20 | 11 31 0e 32 2d 35 2d 33 | |.1.2-5-3|
|000058d0| 31 64 0e 28 64 29 0f 20 | 43 6f 6e 6a 75 67 61 74 |1d.(d). |Conjugat|
|000058e0| 65 3a 20 2d 31 30 11 33 | 69 0d 0a 00 20 20 20 20 |e: -10.3|i... |
|000058f0| 20 20 20 20 20 11 31 50 | 72 6f 64 75 63 74 3a 20 | .1P|roduct: |
|00005900| 2d 31 30 30 11 33 69 20 | 20 20 20 20 20 20 20 20 |-100.3i | |
|00005910| 20 20 20 20 20 20 20 20 | 20 20 11 31 50 72 6f 64 | | .1Prod|
|00005920| 75 63 74 3a 20 31 30 30 | 0d 0a 00 0d 0a 00 59 6f |uct: 100|......Yo|
|00005930| 75 20 6d 61 79 20 77 61 | 6e 74 20 74 6f 20 72 65 |u may wa|nt to re|
|00005940| 76 69 65 77 20 10 31 2d | 35 2d 32 0e 65 31 2d 35 |view .1-|5-2.e1-5|
|00005950| 2d 37 0e 47 75 69 64 65 | 64 20 45 78 61 6d 70 6c |-7.Guide|d Exampl|
|00005960| 65 20 37 2e 0f 0d 0a 00 | 53 65 63 74 69 6f 6e 20 |e 7.....|Section |
|00005970| 31 2e 35 20 20 43 6f 6d | 70 6c 65 78 20 4e 75 6d |1.5 Com|plex Num|
|00005980| 62 65 72 73 0d 0b 00 20 | 39 2e 20 20 50 65 72 66 |bers... |9. Perf|
|00005990| 6f 72 6d 20 74 68 65 20 | 69 6e 64 69 63 61 74 65 |orm the |indicate|
|000059a0| 64 20 64 69 76 69 73 69 | 6f 6e 20 61 6e 64 20 77 |d divisi|on and w|
|000059b0| 72 69 74 65 20 79 6f 75 | 72 20 61 6e 73 77 65 72 |rite you|r answer|
|000059c0| 20 69 6e 20 73 74 61 6e | 64 61 72 64 20 66 6f 72 | in stan|dard for|
|000059d0| 6d 2e 0d 0a 00 0d 0b 00 | 20 20 20 20 20 20 20 34 |m.......| 4|
|000059e0| 11 33 69 0d 0b 00 20 20 | 20 20 20 11 34 32 32 32 |.3i... | .4222|
|000059f0| 32 32 32 0d 0b 00 20 20 | 20 20 20 11 31 31 20 2d |222... | .11 -|
|00005a00| 20 33 11 33 69 0d 0a 00 | 0d 0a 00 20 20 20 20 20 | 3.3i...|... |
|00005a10| 20 20 20 20 20 11 31 34 | 20 20 20 20 20 20 20 20 | .14| |
|00005a20| 20 20 20 20 20 20 20 20 | 20 20 20 20 20 20 20 20 | | |
|00005a30| 20 20 20 20 20 20 20 20 | 37 0d 0b 00 20 20 20 20 | |7... |
|00005a40| 20 0e 32 2d 35 2d 34 39 | 61 0e 28 61 29 0f 20 2d | .2-5-49|a.(a). -|
|00005a50| 11 34 32 20 11 31 2b 20 | 34 11 33 69 20 20 20 20 |.42 .1+ |4.3i |
|00005a60| 20 20 20 20 20 20 20 20 | 20 20 20 20 20 20 20 20 | | |
|00005a70| 20 20 11 31 0e 32 2d 35 | 2d 34 39 62 0e 28 62 29 | .1.2-5|-49b.(b)|
|00005a80| 0f 20 11 34 32 32 11 33 | 69 0d 0b 00 20 20 20 20 |. .422.3|i... |
|00005a90| 20 20 20 20 20 20 11 31 | 33 20 20 20 20 20 20 20 | .1|3 |
|00005aa0| 20 20 20 20 20 20 20 20 | 20 20 20 20 20 20 20 20 | | |
|00005ab0| 20 20 20 20 20 20 20 20 | 31 30 0d 0a 00 0d 0b 00 | |10......|
|00005ac0| 20 20 20 20 20 20 20 20 | 20 20 36 20 20 20 32 20 | | 6 2 |
|00005ad0| 20 20 20 20 20 20 20 20 | 20 20 20 20 20 20 20 20 | | |
|00005ae0| 20 20 20 20 20 20 20 20 | 20 20 36 20 20 20 32 0d | | 6 2.|
|00005af0| 0b 00 20 20 20 20 20 0e | 32 2d 35 2d 34 39 63 0e |.. .|2-5-49c.|
|00005b00| 28 63 29 0f 20 2d 11 34 | 32 20 11 31 2b 20 11 34 |(c). -.4|2 .1+ .4|
|00005b10| 32 11 33 69 20 20 20 20 | 20 20 20 20 20 20 20 20 |2.3i | |
|00005b20| 20 20 20 20 20 20 20 20 | 20 20 11 31 0e 32 2d 35 | | .1.2-5|
|00005b30| 2d 34 39 64 0e 28 64 29 | 0f 20 11 34 32 20 11 31 |-49d.(d)|. .42 .1|
|00005b40| 2b 20 11 34 32 11 33 69 | 0d 0b 00 20 20 20 20 20 |+ .42.3i|... |
|00005b50| 20 20 20 20 20 11 31 35 | 20 20 20 35 20 20 20 20 | .15| 5 |
|00005b60| 20 20 20 20 20 20 20 20 | 20 20 20 20 20 20 20 20 | | |
|00005b70| 20 20 20 20 20 20 20 35 | 20 20 20 35 0d 0a 00 0d | 5| 5....|
|00005b80| 0a 00 59 6f 75 20 6d 61 | 79 20 77 61 6e 74 20 74 |..You ma|y want t|
|00005b90| 6f 20 72 65 76 69 65 77 | 20 10 31 2d 35 2d 32 0e |o review| .1-5-2.|
|00005ba0| 65 31 2d 35 2d 38 0e 47 | 75 69 64 65 64 20 45 78 |e1-5-8.G|uided Ex|
|00005bb0| 61 6d 70 6c 65 20 38 2e | 0f 0d 0a 00 14 00 00 00 |ample 8.|........|
|00005bc0| 7a 00 00 00 50 00 04 00 | 14 00 00 00 10 00 00 00 |z...P...|........|
|00005bd0| 32 2d 35 2d 31 39 61 00 | 92 00 00 00 59 00 00 00 |2-5-19a.|....Y...|
|00005be0| 50 00 04 00 92 00 00 00 | 8e 00 00 00 32 2d 35 2d |P.......|....2-5-|
|00005bf0| 31 39 62 00 ef 00 00 00 | 7a 00 00 00 50 00 04 00 |19b.....|z...P...|
|00005c00| ef 00 00 00 eb 00 00 00 | 32 2d 35 2d 31 39 63 00 |........|2-5-19c.|
|00005c10| 6d 01 00 00 7a 00 00 00 | 50 00 04 00 6d 01 00 00 |m...z...|P...m...|
|00005c20| 69 01 00 00 32 2d 35 2d | 31 39 64 00 eb 01 00 00 |i...2-5-|19d.....|
|00005c30| 4f 01 00 00 50 00 04 00 | eb 01 00 00 e7 01 00 00 |O...P...|........|
|00005c40| 32 2d 35 2d 32 39 61 00 | 3e 03 00 00 ad 00 00 00 |2-5-29a.|>.......|
|00005c50| 50 00 04 00 3e 03 00 00 | 3a 03 00 00 32 2d 35 2d |P...>...|:...2-5-|
|00005c60| 32 39 62 00 ef 03 00 00 | 4f 01 00 00 50 00 04 00 |29b.....|O...P...|
|00005c70| ef 03 00 00 eb 03 00 00 | 32 2d 35 2d 32 39 63 00 |........|2-5-29c.|
|00005c80| 42 05 00 00 87 00 00 00 | 50 00 04 00 42 05 00 00 |B.......|P...B...|
|00005c90| 3e 05 00 00 32 2d 35 2d | 32 39 64 00 cd 05 00 00 |>...2-5-|29d.....|
|00005ca0| 7e 00 00 00 50 00 04 00 | cd 05 00 00 c9 05 00 00 |~...P...|........|
|00005cb0| 32 2d 35 2d 33 31 61 00 | 4f 06 00 00 7e 00 00 00 |2-5-31a.|O...~...|
|00005cc0| 50 00 04 00 4f 06 00 00 | 4b 06 00 00 32 2d 35 2d |P...O...|K...2-5-|
|00005cd0| 33 31 62 00 d1 06 00 00 | a0 00 00 00 50 00 04 00 |31b.....|....P...|
|00005ce0| d1 06 00 00 cd 06 00 00 | 32 2d 35 2d 33 31 63 00 |........|2-5-31c.|
|00005cf0| 75 07 00 00 4c 00 00 00 | 50 00 04 00 75 07 00 00 |u...L...|P...u...|
|00005d00| 71 07 00 00 32 2d 35 2d | 33 31 64 00 c5 07 00 00 |q...2-5-|31d.....|
|00005d10| 39 02 00 00 50 00 04 00 | c5 07 00 00 c1 07 00 00 |9...P...|........|
|00005d20| 32 2d 35 2d 33 35 61 00 | 02 0a 00 00 39 02 00 00 |2-5-35a.|....9...|
|00005d30| 50 00 04 00 02 0a 00 00 | fe 09 00 00 32 2d 35 2d |P.......|....2-5-|
|00005d40| 33 35 62 00 3f 0c 00 00 | 39 02 00 00 50 00 04 00 |35b.?...|9...P...|
|00005d50| 3f 0c 00 00 3b 0c 00 00 | 32 2d 35 2d 33 35 63 00 |?...;...|2-5-35c.|
|00005d60| 7c 0e 00 00 69 00 00 00 | 50 00 04 00 7c 0e 00 00 ||...i...|P...|...|
|00005d70| 78 0e 00 00 32 2d 35 2d | 33 35 64 00 e9 0e 00 00 |x...2-5-|35d.....|
|00005d80| 66 01 00 00 50 00 04 00 | e9 0e 00 00 e5 0e 00 00 |f...P...|........|
|00005d90| 32 2d 35 2d 33 39 61 00 | 53 10 00 00 4c 00 00 00 |2-5-39a.|S...L...|
|00005da0| 50 00 04 00 53 10 00 00 | 4f 10 00 00 32 2d 35 2d |P...S...|O...2-5-|
|00005db0| 33 39 62 00 a3 10 00 00 | 66 01 00 00 50 00 04 00 |39b.....|f...P...|
|00005dc0| a3 10 00 00 9f 10 00 00 | 32 2d 35 2d 33 39 63 00 |........|2-5-39c.|
|00005dd0| 0d 12 00 00 66 01 00 00 | 50 00 04 00 0d 12 00 00 |....f...|P.......|
|00005de0| 09 12 00 00 32 2d 35 2d | 33 39 64 00 77 13 00 00 |....2-5-|39d.w...|
|00005df0| 3a 00 00 00 50 00 04 00 | 77 13 00 00 73 13 00 00 |:...P...|w...s...|
|00005e00| 32 2d 35 2d 33 61 00 b5 | 13 00 00 d6 00 00 00 50 |2-5-3a..|.......P|
|00005e10| 00 04 00 b5 13 00 00 b1 | 13 00 00 32 2d 35 2d 33 |........|...2-5-3|
|00005e20| 62 00 8f 14 00 00 2c 01 | 00 00 50 00 04 00 8f 14 |b.....,.|..P.....|
|00005e30| 00 00 8b 14 00 00 32 2d | 35 2d 33 63 00 bf 15 00 |......2-|5-3c....|
|00005e40| 00 2a 01 00 00 50 00 04 | 00 bf 15 00 00 bb 15 00 |.*...P..|........|
|00005e50| 00 32 2d 35 2d 33 64 00 | ed 16 00 00 a0 02 00 00 |.2-5-3d.|........|
|00005e60| 50 00 04 00 ed 16 00 00 | e9 16 00 00 32 2d 35 2d |P.......|....2-5-|
|00005e70| 34 39 61 00 91 19 00 00 | a0 02 00 00 50 00 04 00 |49a.....|....P...|
|00005e80| 91 19 00 00 8d 19 00 00 | 32 2d 35 2d 34 39 62 00 |........|2-5-49b.|
|00005e90| 35 1c 00 00 90 00 00 00 | 50 00 04 00 35 1c 00 00 |5.......|P...5...|
|00005ea0| 31 1c 00 00 32 2d 35 2d | 34 39 63 00 c9 1c 00 00 |1...2-5-|49c.....|
|00005eb0| a0 02 00 00 50 00 04 00 | c9 1c 00 00 c5 1c 00 00 |....P...|........|
|00005ec0| 32 2d 35 2d 34 39 64 00 | 6d 1f 00 00 38 02 00 00 |2-5-49d.|m...8...|
|00005ed0| 50 00 04 00 6d 1f 00 00 | 69 1f 00 00 32 2d 35 2d |P...m...|i...2-5-|
|00005ee0| 35 31 61 00 a9 21 00 00 | 38 02 00 00 50 00 04 00 |51a..!..|8...P...|
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|00005f00| e5 23 00 00 38 02 00 00 | 50 00 04 00 e5 23 00 00 |.#..8...|P....#..|
|00005f10| e1 23 00 00 32 2d 35 2d | 35 31 63 00 21 26 00 00 |.#..2-5-|51c.!&..|
|00005f20| 8d 00 00 00 50 00 04 00 | 21 26 00 00 1d 26 00 00 |....P...|!&...&..|
|00005f30| 32 2d 35 2d 35 31 64 00 | b2 26 00 00 78 02 00 00 |2-5-51d.|.&..x...|
|00005f40| 50 00 04 00 b2 26 00 00 | ae 26 00 00 32 2d 35 2d |P....&..|.&..2-5-|
|00005f50| 35 39 61 00 2e 29 00 00 | 63 01 00 00 50 00 04 00 |59a..)..|c...P...|
|00005f60| 2e 29 00 00 2a 29 00 00 | 32 2d 35 2d 35 39 62 00 |.)..*)..|2-5-59b.|
|00005f70| 95 2a 00 00 78 02 00 00 | 50 00 04 00 95 2a 00 00 |.*..x...|P....*..|
|00005f80| 91 2a 00 00 32 2d 35 2d | 35 39 63 00 11 2d 00 00 |.*..2-5-|59c..-..|
|00005f90| 78 02 00 00 50 00 04 00 | 11 2d 00 00 0d 2d 00 00 |x...P...|.-...-..|
|00005fa0| 32 2d 35 2d 35 39 64 00 | 8d 2f 00 00 d7 00 00 00 |2-5-59d.|./......|
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|00005fc0| 39 61 00 68 30 00 00 6e | 00 00 00 50 00 04 00 68 |9a.h0..n|...P...h|
|00005fd0| 30 00 00 64 30 00 00 32 | 2d 35 2d 39 62 00 da 30 |0..d0..2|-5-9b..0|
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|00005ff0| 00 00 32 2d 35 2d 39 63 | 00 b5 31 00 00 d7 00 00 |..2-5-9c|..1.....|
|00006000| 00 50 00 04 00 b5 31 00 | 00 b1 31 00 00 32 2d 35 |.P....1.|..1..2-5|
|00006010| 2d 39 64 00 90 32 00 00 | 6e 00 00 00 50 00 04 00 |-9d..2..|n...P...|
|00006020| 90 32 00 00 8c 32 00 00 | 61 32 2d 35 2d 31 31 61 |.2...2..|a2-5-11a|
|00006030| 00 02 33 00 00 61 00 00 | 00 50 00 04 00 02 33 00 |..3..a..|.P....3.|
|00006040| 00 fe 32 00 00 61 32 2d | 35 2d 31 31 62 00 67 33 |..2..a2-|5-11b.g3|
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|00006060| 00 00 61 32 2d 35 2d 31 | 31 63 00 cc 33 00 00 61 |..a2-5-1|1c..3..a|
|00006070| 00 00 00 50 00 04 00 cc | 33 00 00 c8 33 00 00 61 |...P....|3...3..a|
|00006080| 32 2d 35 2d 31 31 64 00 | 31 34 00 00 12 01 00 00 |2-5-11d.|14......|
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|000060a0| 2d 32 31 61 00 47 35 00 | 00 7a 00 00 00 50 00 04 |-21a.G5.|.z...P..|
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|000060c0| 62 00 c5 35 00 00 12 01 | 00 00 50 00 04 00 c5 35 |b..5....|..P....5|
|000060d0| 00 00 c1 35 00 00 61 32 | 2d 35 2d 32 31 63 00 db |...5..a2|-5-21c..|
|000060e0| 36 00 00 12 01 00 00 50 | 00 04 00 db 36 00 00 d7 |6......P|....6...|
|000060f0| 36 00 00 61 32 2d 35 2d | 32 31 64 00 f1 37 00 00 |6..a2-5-|21d..7..|
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|00006110| 61 32 2d 35 2d 34 31 61 | 00 3a 38 00 00 89 00 00 |a2-5-41a|.:8.....|
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|00006130| 35 2d 34 31 62 00 c7 38 | 00 00 96 00 00 00 50 00 |5-41b..8|......P.|
|00006140| 04 00 c7 38 00 00 c3 38 | 00 00 61 32 2d 35 2d 34 |...8...8|..a2-5-4|
|00006150| 31 63 00 61 39 00 00 3b | 00 00 00 50 00 04 00 61 |1c.a9..;|...P...a|
|00006160| 39 00 00 5d 39 00 00 61 | 32 2d 35 2d 34 31 64 00 |9..]9..a|2-5-41d.|
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|00006180| 9c 39 00 00 61 32 2d 35 | 2d 34 33 61 00 83 3b 00 |.9..a2-5|-43a..;.|
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|000061e0| 34 33 64 00 fd 3d 00 00 | 12 02 00 00 4d 1c 00 00 |43d..=..|....M...|
|000061f0| e1 3d 00 00 00 00 00 00 | 78 31 2d 35 00 2b 40 00 |.=......|x1-5.+@.|
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|00006210| 00 78 31 2d 35 2d 31 00 | 9b 41 00 00 45 02 00 00 |.x1-5-1.|.A..E...|
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|00006230| 2d 31 30 00 fc 43 00 00 | a6 01 00 00 4d 1c 00 00 |-10..C..|....M...|
|00006240| e0 43 00 00 00 00 00 00 | 78 31 2d 35 2d 31 31 00 |.C......|x1-5-11.|
|00006250| be 45 00 00 a2 02 00 00 | 4d 1c 00 00 a2 45 00 00 |.E......|M....E..|
|00006260| 00 00 00 00 78 31 2d 35 | 2d 31 32 00 7c 48 00 00 |....x1-5|-12.|H..|
|00006270| 4e 01 00 00 4d 1c 00 00 | 60 48 00 00 00 00 00 00 |N...M...|`H......|
|00006280| 78 31 2d 35 2d 31 33 00 | e6 49 00 00 ed 01 00 00 |x1-5-13.|.I......|
|00006290| 4d 1c 00 00 ca 49 00 00 | 00 00 00 00 78 31 2d 35 |M....I..|....x1-5|
|000062a0| 2d 31 34 00 ef 4b 00 00 | 53 01 00 00 4d 1c 00 00 |-14..K..|S...M...|
|000062b0| d3 4b 00 00 00 00 00 00 | 78 31 2d 35 2d 32 00 5e |.K......|x1-5-2.^|
|000062c0| 4d 00 00 4a 02 00 00 4d | 1c 00 00 42 4d 00 00 00 |M..J...M|...BM...|
|000062d0| 00 00 00 78 31 2d 35 2d | 33 00 c4 4f 00 00 58 01 |...x1-5-|3..O..X.|
|000062e0| 00 00 4d 1c 00 00 a8 4f | 00 00 00 00 00 00 78 31 |..M....O|......x1|
|000062f0| 2d 35 2d 34 00 38 51 00 | 00 9b 01 00 00 4d 1c 00 |-5-4.8Q.|.....M..|
|00006300| 00 1c 51 00 00 00 00 00 | 00 78 31 2d 35 2d 35 00 |..Q.....|.x1-5-5.|
|00006310| ef 52 00 00 b7 01 00 00 | 4d 1c 00 00 d3 52 00 00 |.R......|M....R..|
|00006320| 00 00 00 00 78 31 2d 35 | 2d 36 00 c2 54 00 00 bb |....x1-5|-6..T...|
|00006330| 02 00 00 4d 1c 00 00 a6 | 54 00 00 00 00 00 00 78 |...M....|T......x|
|00006340| 31 2d 35 2d 37 00 99 57 | 00 00 cf 01 00 00 4d 1c |1-5-7..W|......M.|
|00006350| 00 00 7d 57 00 00 00 00 | 00 00 78 31 2d 35 2d 38 |..}W....|..x1-5-8|
|00006360| 00 84 59 00 00 38 02 00 | 00 4d 1c 00 00 68 59 00 |..Y..8..|.M...hY.|
|00006370| 00 00 00 00 00 78 31 2d | 35 2d 39 00 |.....x1-|5-9. |
+--------+-------------------------+-------------------------+--------+--------+
