Ricordiamo le operazioni tra numeri complessi in forma esponenziale:

Siano $\displaystyle z_1=\rho_1 e^{i\vartheta_1}$ e $\displaystyle z_2=\rho_2 e^{i\vartheta_2}$

Moltiplicazione

$\displaystyle z_1\cdot z_2=\rho_1\cdot \rho_2e^{i(\vartheta_1+\vartheta_2)}$

Divisione

$\displaystyle \frac{z_1}{z_2} =\frac{\rho_1}{\rho_2}e^{i(\vartheta_1-\vartheta_2)}$

Potenza

$\displaystyle z^n=\rho^ne^{in\vartheta}$

Siano $\displaystyle z_1=3 e^{i\pi}$ e $\displaystyle z_2=2 e^{i\frac{\pi}{2}}$

$\displaystyle z_1\cdot z_2=6e^{i(\pi+\frac{\pi}{2})}=6e^{i\frac{3}{2}\pi}$

$\displaystyle \frac{z_1}{z_2} =\frac{3}{2}e^{i(\pi-\frac{\pi}{2})}=\frac{3}{2}e^{i\frac{\pi}{2}}$

$\displaystyle z_1^5=243e^{i5\pi}$