# Power of complex numbers

$z=a+ib;a,b\in \mathrm{ℝ},i=\sqrt{-1}$
$r=\sqrt{{a}^{2}+{b}^{2}},tg\phi =\frac{b}{a}\left(a\ne 0\right)$
$z=r·{e}^{\phi i}=r·\left(\mathrm{cos}\phi +i·\mathrm{sin}\phi \right)$
Keywords: power of complex numbers