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)

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