If $\arg (\mathrm{z})<0$, then $\arg (-\mathrm{z})-\arg (\mathrm{z})$ equals

If $\arg (\mathrm{z})<0$, then $\arg (-\mathrm{z})-\arg (\mathrm{z})$ equals
  1. $\frac{\pi}{2}$
  2. $-\frac{\pi}{2}$
  3. $\pi$
  4. $-\pi$

Solution

$\begin{aligned} & \arg (-\mathrm{z})-\arg (\mathrm{z}) \\ & =\arg (-1 \times \mathrm{z})-\arg (\mathrm{z}) \\ & =\arg (-1)+\arg (\mathrm{z})-\arg (\mathrm{z}) \\ & =\pi\end{aligned}$

Asked in: MHT CET 2022 (05 Aug Shift 1)

Practice more Complex Number questions on Aicharya