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If z is a complex number of unit modulus and argument $\theta$ , the $arg\left[\frac{1+z}{1+\overline{z}}\right]$ is equal to

A) -

$\theta$

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

$\theta$

$\pi-\theta$

Option C

Given , |z|=1, arg z= $\theta$ $\therefore$ z = $e^{i\theta}$

But $\overline{z}=\frac{1}{z}$

$\therefore$ $arg\left[\frac{1+z}{1+\frac{1}{z}}\right]=arg(z)=\theta$

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