Question

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

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

Answer 1

Answer: (C)

$\theta$

Answer 2

The correct option is(C): θ.

Given, |z | = 1, arg 2 =$\theta \therefore \, z=e^{i\theta}$
But $\bar{z}=\frac{1}{z}$
$\therefore arg \bigg( \frac{1+z}{1+\frac{1}{2}}\bigg)=arg (z) =\theta$