1) 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) -$\theta$ B) $\frac{\pi}{2}-\theta$ C) $\theta$ D) $\pi-\theta$ Answer: Option CExplanation:Given , |z|=1, arg z= $\theta$ $\therefore$ z = $e^{i\theta}$ But $\overline{z}=\frac{1}{z}$ $\therefore$ $arg\left[\frac{1+z}{1+\frac{1}{z}}\right]=arg(z)=\theta$
