If z is a complex number of unit modulus and argument , then (1+z1+ z) equals:

Question

If $z$ is a complex number of unit modulus and argument $	heta$, then $\arg\left(\dfrac{1+z}{1+\bar z}ight)$ equals:

Accepted Answer

Since $|z|=1$, $\bar z=\dfrac1z$.

$$\arg\left(\frac{1+z}{1+\bar z}\right)=\arg\left(\frac{1+z}{1+\frac1z}\right)=\arg(z)=\theta.$$

Solutions · 1