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If $-\pi < \arg (z) < -\frac{\pi}{2}$ then $\arg \bar{z}-\arg (-\bar{z})$ is
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1313 Upvotes
Verified Answer
The correct answer is:
$\pi$
Hints: 
$$
\begin{aligned}
& \text { if } \arg (z)=-\pi+\theta \\
& \Rightarrow \arg (\bar{z})=\pi-\theta \\
& \arg (-\bar{z})=-\theta \\
& \arg (\bar{z})-\arg (-\bar{z})=\pi-\theta-(-\theta)=\pi-\theta+\theta=\pi
\end{aligned}
$$
$$
\begin{aligned}
& \text { if } \arg (z)=-\pi+\theta \\
& \Rightarrow \arg (\bar{z})=\pi-\theta \\
& \arg (-\bar{z})=-\theta \\
& \arg (\bar{z})-\arg (-\bar{z})=\pi-\theta-(-\theta)=\pi-\theta+\theta=\pi
\end{aligned}
$$
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