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