-- stack: in
-- format: 10 (HyperCard 2)
-- flags: 0x1000 (none)
-- protect password hash: 0
-- maximum user level: 5 (scripting)
-- window: Rect(x1=112, y1=113, x2=528, y2=353)
-- screen: Rect(x1=0, y1=0, x2=640, y2=480)
-- card dimensions: w=416 h=240
-- scroll: x=0 y=0
-- background count: 1
-- first background id: 2754
-- card count: 1
-- first card id: 3602
-- list block id: 2156
-- print block id: 0
-- font table block id: 3385
-- style table block id: 3183
-- free block count: 5
-- free size: 5728 bytes
-- total size: 16384 bytes
-- stack block size: 6656 bytes
-- created by hypercard version: 0x02418000
-- compacted by hypercard version: 0x02418000
-- modified by hypercard version: 0x02418000
-- opened by hypercard version: 0x02418000
-- patterns[0]: 0x0000000000000000
-- patterns[1]: 0x8000000008000000
-- patterns[2]: 0x8800220088002200
-- patterns[3]: 0x8888222288882222
-- patterns[4]: 0x88AA22AA88AA22AA
-- patterns[5]: 0xCCAA33AACCAA33AA
-- patterns[6]: 0xEEAABBAAEEAABBAA
-- patterns[7]: 0xEEBBBBEEEEBBBBEE
-- patterns[8]: 0xFFBBFFEEFFBBFFEE
-- patterns[9]: 0xFFBBFFFFFFBBFFFF
-- patterns[10]: 0x8010022001084004
-- patterns[11]: 0xFFFFFFFFFFFFFFFF
-- patterns[12]: 0x8822882288228822
-- patterns[13]: 0x1122448811224488
-- patterns[14]: 0xC4800C6843023026
-- patterns[15]: 0xB130031BD8C00C8D
-- patterns[16]: 0xAA00AA00AA00AA00
-- patterns[17]: 0x8822552288225522
-- patterns[18]: 0x8855225588552255
-- patterns[19]: 0x77DD77DD77DD77DD
-- patterns[20]: 0x8000000000000000
-- patterns[21]: 0xAA55AA55AA55AA55
-- patterns[22]: 0x038448300C020101
-- patterns[23]: 0x8244394482010101
-- patterns[24]: 0x8814224188412214
-- patterns[25]: 0x8080413E080814E3
-- patterns[26]: 0x22048C7422179810
-- patterns[27]: 0xBE808808EB088880
-- patterns[28]: 0x25C8328964244C92
-- patterns[29]: 0xA29C41BE2AC914EB
-- patterns[30]: 0x40A00000040A0000
-- patterns[31]: 0x8040200002040800
-- patterns[32]: 0xAA00800088008000
-- patterns[33]: 0xFF80808080808080
-- patterns[34]: 0x081C22C180010204
-- patterns[35]: 0xFF808080FF080808
-- patterns[36]: 0xF87422478F172271
-- patterns[37]: 0xBF00BFBFB0B0B0B0
-- patterns[38]: 0xFF7FBE5DA2418000
-- patterns[39]: 0xFAF5FAF5A050A050
-- checksum: 0xDDA1A3F7
----- HyperTalk script -----
function complexNumbers a,b,o,c,d
if o = "+" then return (a+c)&(the itemdelimiter)&(b+d)
if o = "-" then return (a-c)&(the itemdelimiter)&(b-d)
if o = "*" then return ((a*c)-(b*d))&(the itemdelimiter)&((b*c)+(c*d))
if o = "/" then return (((a*c)/((c^2)+(d^2)))+((b*d)/((c^2)+(d^2))))&(the itemdelimiter)&(((b*c)/((c^2)+(d^2)))+((c*d)/(((c^2)+(d^2))^2)))
if o = "\" or h = "div" then return (((a*c)DIV((c^2)+(d^2)))+((b*d)DIV((c^2)+(d^2))))&(the itemdelimiter)&(((b*c)DIV((c^2)+(d^2)))+((c*d)DIV(((c^2)+(d^2))^2)))
if o = "mod" then return (((a*c)MOD((c^2)+(d^2)))+((b*d)MOD((c^2)+(d^2))))&(the itemdelimiter)&(((b*c)MOD((c^2)+(d^2)))+((c*d)MOD(((c^2)+(d^2))^2)))
if o = "^" then return exp((c*ln(sqrt((a^2)+(b^2))))-(d*theta(a,b)))*cos((d*ln(sqrt((a^2)+(b^2))))+(c*theta(a,b)))&(the itemdelimiter)&exp((c*ln(sqrt((a^2)+(b^2))))-(d*theta(a,b)))*sin((d*ln(sqrt((a^2)+(b^2))))+(c*theta(a,b)))
if o = "√" or h = "root" then return complexNumbers(a,b,"^",c/((c^2)+(d^2)),d/((c^2)+(d^2)))

if a = "|" or a = "abs" then return sqrt((b^2)+(o^2))&(the itemdelimiter)&"0"
if a = "sin" then return sin(b)*cosh(o)&(the itemdelimiter)&cos(b)*sinh(o)
if a = "cos" then return cos(b)*cosh(o)&(the itemdelimiter)&sin(b)*sinh(o)
if a = "tan" then return complexnumbers(sin(b)*cosh(o),cos(b)*sinh(o),"/",cos(b)*cosh(o),sin(b)*sinh(o))
if a = "atan" then return ((theta(1-o,b)/2)-(theta(1+o,-b)/2))&(the itemdelimiter)&(ln(((b^2)+((o+1)^2))/((b^2)+((o-1)^2)))/4)
if a = "/" then return (b/((b^2)+(o^2)))&(the itemdelimiter)&(o/((b^2)+(o^2)))
if a = "ln" or a = "log" or a = "loge" then
  if c is a number then return ln(abs(b))&(the itemdelimiter)&(theta(b,o)+(2*pi*c))
  return ln(abs(b))&(the itemdelimiter)&theta(b,o)
end if
if a = "log2" then return complexNumbers(item 1 of complexNumbers("ln",b,o,c),item 2 of complexNumbers("ln",b,o,c),"/",ln(2),0)
if a = "log10" then return complexNumbers(item 1 of complexNumbers("ln",b,o,c),item 2 of complexNumbers("ln",b,o,c),"/",ln(10),0)
if a = "exp" then return (exp(b)*cos(o))&(the itemdelimiter)&(cos(o)*sin(o))
if a = "√" or a = "sqrt" or a = "sqr" then return complexnumbers(b,o,"^",0.5,0)
if a = "sgn" then
  if b < 0 then put "-1" into ta
  if b > 0 then put "1" into ta
  if b = 0 then put "0" into ta
  put (the itemdelimiter) after ta
  if o > 0 then put "1" after ta
  if o < 0 then put "-1" after ta
  if o = 0 then put "0" after ta
  return ta
end if
if a = "P>R" then return (b*cos(o))&(the itemdelimiter)&(b*sin(o))
if a = "R>P" then return sqrt((b^2)+(o^2))&(the itemdelimiter)&theta(b,o)
if a = "BC" or a = "BaseConv" or a = "BaseConvert" or a = "BaseConvertReal" then
  put baseconvertreal(b,c,d) into ta
  put (the itemdelimiter) after ta
  put baseconvertreal(o,c,d) after ta
  return ta
end if

return "Error: Unsupported operation."
end complexNumbers

function cn l,m,n,o,p
return complexNumbers(l,m,n,o,p)
end cn

function cpxAdd a,b,c,d
return cn(a,b,"+",c,d)
end cpxAdd

function cpxSub a,b,c,d
return cn(a,b,"-",c,d)
end cpxSub

function cpxMul a,b,c,d
return cn(a,b,"*",c,d)
end cpxMul

function cpxDiv a,b,c,d
return cn(a,b,"/",c,d)
end cpxDiv

function cpxPower a,b,c,d
return cn(a,b,"^",c,d)
end cpxPower

function cpxLog a,b,v
return cn("ln",a,b,v)
end cpxlog

function cpxExp a,b
return cn("exp",a,b)
end cpxExp

function cpxSin a,b
return cn("sin",a,b)
end cpxSin

function cpxCos a,b
return cn("cos",a,b)
end cpxCos

function cpxAbs a,b
return cn("|",a,b)
end cpxAbs

function cpxRecip a,b
return cn("/",a,b)
end cpxRecip

function cpxSgn a,b
return cn("sgn",a,b)
end cpxSgn

function cpxIntDiv a,b,c,d
return cn(a,b,"\",c,d)
end cpxIntDiv

function cpxMod a,b,c,d
return cn(a,b,"mod",c,d)
end cpxMod

function cpxSqrt a,b
return cn("sqrt",a,b)
end cpxSqrt

function cpxRoot a,b,c,d
return cn(a,b,"√",c,d)
end cpxRoot

function cpxTan a,b
return cn("tan",a,b)
end cpxTan

function cpxstrtoval x
put the itemdelimiter into z
if x is a number then return (x*1)&z&"0"
if the last char of x <> "i" then return "ERROR: Expected complex number here."
if "+" is not in x and "-" is not in x then
  delete last char of x
  return "0"&z&(x*1)
end if
if "+" is in x and "-+" is not in x then
  set the itemdelimiter to "+"
  delete last char of x
  put ((item 1 of x)*1)&z&((item 2 of x)*1) into y
  set the itemdelimiter to z
  return y
end if
if the first char of x is "-" and "+-" is not in x then
  set the itemdelimiter to "-"
  delete last char of x
  put ((item 2 of x)*-1)&z&-((item 3 of x)*1) into y
  set the itemdelimiter to z
  return y
end if
if "-" is in x and "+-" is not in x then
  set the itemdelimiter to "-"
  delete last char of x
  put ((item 1 of x)*1)&z&-((item 2 of x)*1) into y
  set the itemdelimiter to z
  return y
end if
end cpxstrtoval

function cpxvaltostr a,b
put a into x
if b<0 then put b after x
if b=0 or b>0 then put "+" & b after x
put "i" after x
return x
end cpxvaltostr