Discussion Forum

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

Answer:

Explanation:

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

  But   $\overline{z}=\frac{1}{z}$

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