Komplexa tal i polär form

Produkt av komplexa tal i polär form

\begin{align*}
z\cdot w &= r_1 (\cos(\theta) +\mathrm{i} \sin(\theta) ) \cdot r_2(\cos(\psi) +\mathrm{i}
\sin(\psi))\\
&=r_1\cdot r_2(\cos(\theta +\psi) +\mathrm{i} \sin(\theta +\psi))
\end{align*}

Division av komplexa tal i polär form

\begin{align*}
\frac{z}{w} &= \frac{r_1 (\cos(\theta) +\mathrm{i} \sin(\theta) )}{ r_2(\cos(\psi) +\mathrm{i}
\sin(\psi))}\\
&=\frac{r_1}{ r_2}(\cos(\theta -\psi) +\mathrm{i} \sin(\theta -\psi))
\end{align*}