Answer
$z=a+bi$
So, $z+\frac{}{z}$ is a real number
Work Step by Step
$z=a+bi$
Find the conjugate of the complex numbers by changing the sign of their imaginary part:
$\frac{}{z}=a-bi$
$z+\frac{}{z}=a+bi+a-bi=2a$
Therefore, $z+\frac{}{z}$ is a real number
