The amplitude of 1 i is equal to: - Vidyadip

MCQ

The amplitude of $\frac{1}{\text{i}}$ is equal to:

A
$0$
B
$\frac{\pi}{2}$
✓
$-\frac{\pi}{2}$
D
$\pi$

✓

Answer

Correct option: C.

$-\frac{\pi}{2}$

Let $\text{z}=\frac{1}{\text{i}}$
$\text{z}=\frac{1}{\text{i}}\times\frac{\text{i}}{\text{i}}$
$\text{z}=\frac{\text{i}}{\text{i}^2}$
$\text{z}=-\text{i}$
Since, $z (0, -1)$ lies on the negative imaginary axis .
Therefore, $\text{arg(z)}=\frac{-\pi}{2}$

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