Absolute Value

The absolute value of a complex number z, the distance of z from zero, is denoted $\left\vert\vphantom{ \,z}\right.$ z$\left.\vphantom{ \,z}\right\vert$.

$\blacktriangleright$ To put vertical bars around an expression

1.
Select the expression with the mouse.

2.
Click itbpF0.2992in0.2992in0.0692infences.wmf or choose Insert + Brackets.

3.
Select the vertical bar.


4.
Choose OK.

$\blacktriangleright$ To take the absolute value of a complex number

1.
Place the insertion point in an expression enclosed between vertical bars.

2.
Choose Evaluate.

$\blacktriangleright$ Evaluate

$\left\vert\vphantom{ a+bi}\right.$a + bi$\left.\vphantom{ a+bi}\right\vert$ = $\sqrt{{\left( a^{2}+b^{2}\right) }}$


$\left\vert\vphantom{ 2+3i}\right.$2 + 3i$\left.\vphantom{ 2+3i}\right\vert$ =  $\sqrt{{13}}$


$\left\vert\vphantom{ \sqrt{1+2i}}\right.$$\sqrt{{1+2i}}$$\left.\vphantom{ \sqrt{1+2i}}\right\vert$ = $\sqrt[4]{{5}}$


$\left\vert\vphantom{ 2.5-16.3i}\right.$2.5 - 16.3i$\left.\vphantom{ 2.5-16.3i}\right\vert$ = 16. 491


$\left\vert\vphantom{ e^{i\pi }}\right.$eiπ$\left.\vphantom{ e^{i\pi }}\right\vert$ =  1

$\blacktriangleright$ Evaluate Numerically

$\left\vert\vphantom{ 2+3i}\right.$2 + 3i$\left.\vphantom{ 2+3i}\right\vert$ = 3. 6056


$\left\vert\vphantom{ \sqrt{1+2i}}\right.$$\sqrt{{1+2i}}$$\left.\vphantom{ \sqrt{1+2i}}\right\vert$ = 1. 4953