## Precalculus: Mathematics for Calculus, 7th Edition

$z=a+bi$ So, $z-\frac{}{z}$ is a pure imaginary number.
$z=a+bi$ 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.