Precalculus: Mathematics for Calculus, 7th Edition

$z=a+bi$ So, $\frac{}{z}=a-bi$ $z=\frac{}{z}$ if and only if z is real
$z=a+bi$ 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