Prove the following for any two complex numbers $z$ and $w$, with $w\ne0$:

\[\frac{z}{w} = \frac{zw^*}{|w|^2}.\]

Question

Prove the following for any two complex numbers $z$ and $w$, with $w\ne0$: $$\frac{z}{w} = \frac{zw^*}{|w|^2}.$$

Accepted Answer

$\frac zw=\frac{zw^*}{|w|^2}$, since $ww^*=|w|^2>0$.

Realizing complex division via conjugation