The argument of every complex number is: - Vidyadip

MCQ

The argument of every complex number is:

A
Double valued
B
Single valued
✓
Many valued
D
Triple valued

✓

Answer

Correct option: C.

Many valued

$z = x + iy$
amplitude $=\tan^{-1}\frac{\text{y}}{\text{x}}$
$\Rightarrow$ amplitude $=\theta\pm2\text{k}\pi$
where $\theta\in[-\pi,\pi]\ \forall\text{k}\in\text{R}$
since $\text{k}\in\text{R}$
$\Rightarrow$ Amplitude of any complex number is many valued.

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