Rappresentare un numero complesso in forma algebrica, trigonometrica ed esponenziale.

a) $\displaystyle z=a+ib$ $\longrightarrow$ (forma algebrica o cartesiana)

$\displaystyle z=3+4i$

b) $\displaystyle z=\rho(\cos \vartheta + i \sin \vartheta)$ $\longrightarrow$ (forma trigonometrica)

$\displaystyle z=\sqrt{2}\left[\cos {\left(\frac{\pi}{4}\right)}+i\sin{\left(\frac{\pi}{4}\right)}\right]$

c) $\displaystyle z=\rho e^{i\vartheta}$ $\longrightarrow$ (forma esponenziale)

$\displaystyle z=\sqrt{2}e^{i\frac{\pi}{4}}$