Euler's formula: $e^{i\theta}=\cos\theta+i\sin\theta$
De Moivre's theorem: $(r e^{i\theta})^n = r^n e^{in\theta}$
Multiplication: $r_1 e^{i\theta_1}\cdot r_2 e^{i\theta_2}=r_1 r_2\, e^{i(\theta_1+\theta_2)}$
Division: $\dfrac{r_1 e^{i\theta_1}}{r_2 e^{i\theta_2}}=\dfrac{r_1}{r_2}\, e^{i(\theta_1-\theta_2)}$
nth roots: $z^{1/n}=r^{1/n} e^{i(\theta+2k\pi)/n},\; k=0,1,\ldots,n{-}1$
$i^2=-1,\quad i^3=-i,\quad i^4=1,\quad e^{i\pi}=-1$