Precalculus: Mathematics for Calculus, 7th Edition

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