Hallo,
\( (5+i)^{19} \)
Satz von Moivre:
\( \begin{array}{c}\mathrm{z}^{\mathrm{n}}=\mathrm{r}^{\mathrm{n}}(\cos (\mathrm{n} \varphi)+i \sin (\mathrm{n} \varphi)) \\ \mathrm{mit} \\ \mathrm{r}=|z|=|\mathrm{a}+i \mathrm{~b}|=\sqrt{\mathrm{a}^{2}+\mathrm{b}^{2}}\end{array} \)
n=19
z=5+i
r= √26
\( \varphi=\arctan \left(\frac{1}{5}\right) \)
\( (5+i)^{19}=5429503678976 \sqrt{26}\left(\cos \left(19 \arctan \left(\frac{1}{5}\right)\right)+i \sin \left(19 \arctan \left(\frac{1}{5}\right)\right)\right) \)