Question

The amplitude of $\frac{1}{i}$ is equal to
(a) 0
(b) $\frac{\mathrm{\pi }}{2}$
(c) $-\frac{\mathrm{\pi }}{2}$
(d) π

Answer 1

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

$$\begin{gathered} \mathrm{Let}z=\frac{1}{i} \\ \Rightarrow z=\frac{1}{i}\times \frac{i}{i} \\ \Rightarrow z=\frac{i}{i^2} \\ \Rightarrow z=-i \end{gathered}$$

$$\begin{gathered} \mathrm{Since},z\left(0,-1\right)\mathrm{lies}\mathrm{on}\mathrm{the}\mathrm{negative}\mathrm{imaginary}\mathrm{axis}. \\ \mathrm{Therefore},\arg \left(z\right)=\frac{-\mathrm{\pi }}{2} \end{gathered}$$