# Inverse of complex number

plexus0208
How does taking the multiplicative inverse (reciprocal) of a complex number change its magnitude and argument?

WiFO215
A complex number z, when inverted, will have its magnitude also inverted, $$|z^{-1}| = \frac{1}{|z|}$$ and its argument will become its supplement, $$arg(z^{-1}) = \pi - arg(z)$$

Why don't you try proving that?