If $-\pi < \arg (z) < -\frac{\pi}{2}$ then $\arg \bar{z}-\arg (-\bar{z})$ is

• Correct answer
  A

  $\pi$
• B

  $\square \pi$
• C

  $\frac{\pi}{2}$
• D

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

Solution

Hints:
$$ \begin{aligned} & \text { if } \arg (z)=-\pi+\theta \\ & \Rightarrow \arg (\bar{z})=\pi-\theta \\ & \arg (-\bar{z})=-\theta \\ & \arg (\bar{z})-\arg (-\bar{z})=\pi-\theta-(-\theta)=\pi-\theta+\theta=\pi \end{aligned} $$

Hence, the correct answer is option: 'A'.