Umocnění komplexního čísla
Umocni komplexní číslo a výsledek zapiš v algebraickém tvaru:
\large z_2 = \left( \Large \frac{3+\text{i}\sqrt {3}}{2}\large \right) ^3
\cos\:\frac{\pi}{2}=0
\sin\:\frac{\pi}{2}=1
\large z_2 = 3\sqrt {3}\left( 0+\text{i}\right) = 3\text{i}\sqrt {3}
\cos\:\frac{\pi}{6}=\frac{\sqrt{3}}{2}
\sin\:\frac{\pi}{6}=\frac{1}{2}
\large z_2 = 3\sqrt {3}\left( \frac{\sqrt{3}}{2}+\text{i}\frac{1}{2}\right) = \frac{9}{2} + \frac{3\sqrt{3}}{2}\text{i}
\cos\:\frac{\pi}{4}=\frac{\sqrt{2}}{2}
\sin\:\frac{\pi}{4}=\frac{\sqrt{2}}{2}
\large z_2 = 3\sqrt {3}\left( \frac{\sqrt{2}}{2}+\text{i}\frac{\sqrt{2}}{2}\right) = \frac{3\sqrt{6}}{2} + \frac{3\sqrt{6}}{2}\text{i}
\cos\:\frac{\pi}{3}=\frac{1}{2}
\sin\:\frac{\pi}{3}=\frac{\sqrt{3}}{2}
\large z_2 = 3\sqrt {3}\left( \frac{1}{2}+\text{i}\frac{\sqrt{3}}{2}\right) = \frac{3}{2}\text{i}\sqrt {3} + \frac{3\sqrt{3}}{2}