# The amplitude of

Question:

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

(a) 0

(b) $\frac{\pi}{2}$

(c) $-\frac{\pi}{2}$

(d) $\pi$

Solution:

(c) $-\frac{\pi}{2}$

Let $z=\frac{1}{i}$

$\Rightarrow z=\frac{1}{i} \times \frac{i}{i}$

$\Rightarrow z=\frac{i}{i^{2}}$

$\Rightarrow z=-i$

Since, $z(0,-1)$ lies on the negative imaginary axis.

Therefore, $\arg (z)=\frac{-\pi}{2}$