JEE Main 2013 (Offline)Question 1
If $z$ is a complex number of unit modulus and argument $\theta$, then $\arg\left(\frac{1+z}{1+\bar z}\right)$ equals :
Complex Numbers
Solution
With $|z|=1$, $1+z=z(\bar z+1)$, so $\frac{1+z}{1+\bar z}=z$ and its argument is $\theta$.