Answer
$z=a+bi$
So, $\frac{}{z}=a-bi$
$z=\frac{}{z}$ if and only if z is real
Work Step by Step
$z=a+bi$
Find the conjugate of the complex numbers by changing the sign of their imaginary part:
$\frac{}{z}=a-bi$
$z=\frac{}{z}$ if and only if the imaginary part is not exist, then $z=\frac{}{z}=a$
Therefore, $z=\frac{}{z}$ if and only if z is real
