Question

If $z$ is a complex number of unit modulus and argument $\theta$, then $\arg \left(\frac{1+z}{1+\overline{z}}\right)$ equals :

• A. $-\theta$
• B. $\frac{\pi }{2}-\theta$
• C. $\theta$
• D. $\pi -\theta$

Answer 1

The correct option is C $\theta$

$|z|=1$ and $\arg \left(z\right)=\theta$
So, $z=e^{i\theta }$
$\arg \left(\frac{1+z}{1+\overline{z}}\right)=\arg \left(\frac{1+z}{1+\frac{1}{z}}\right)$
$=\arg \left(z\right)$
$=\theta$