Question

State true or false
if $z$ is a complex number then $z\overline{z}$ is purely real.

• A. True
• B. False

Answer 1

The correct option is A True

Let $z=a+ib$.

Hence $\overline{z}=a-ib$

So, $z\overline{z}=(a+ib)(a-ib)=a^2+b^2$ which is purely real.