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  4. If -π < arg (z) < -(π/2) then arg barz - arg (- barz) is

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

WBJEEWBJEE 2010Complex Numbers and Quadratic Equations

Solution:

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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 $