Umocnění komplexního čísla
Umocni komplexní číslo a výsledek zapiš v algebraickém tvaru:
\large z_4 = \left( \Large \frac{\sqrt {5}}{2}\large -\Large \frac{\sqrt {15}}{2}\large \text{i}\right) ^7
\cos\frac{5\pi}{3}=\frac12
sin\frac{5\pi}{3}=-\frac{\sqrt3}{2}
\large z_4 = 125\sqrt {5}\left( \Large \frac{1}{2}\large -\Large \frac{\sqrt {3}}{2}\large \text{i}\right) = \Large \frac{125\sqrt {5}}{2}\large -\Large \frac{125\sqrt {15}}{2}\large \text{i}
\cos\frac{5\pi}{3}=\frac12
sin\frac{5\pi}{3}=\frac{\sqrt3}{2}
\large z_4 = 125\sqrt {5}\left( \Large \frac{1}{2}\large -\Large \frac{\sqrt {3}}{2}\large \text{i}\right) = \Large \frac{125\sqrt {5}}{2}\large -\Large \frac{125\sqrt {15}}{2}\large \text{i}
\cos\frac{5\pi}{3}=\frac{3}{2}
sin\frac{5\pi}{3}=-\frac{\sqrt3}{2}
\large z_4 = 125\sqrt {5}\left( \Large \frac{1}{2}\large -\Large \frac{\sqrt {3}}{2}\large \text{i}\right) = \Large \frac{125\sqrt {5}}{2}\large -\Large \frac{125\sqrt {15}}{2}\large \text{i}
\cos\frac{5\pi}{3}=\frac12
sin\frac{5\pi}{3}=-\frac{\sqrt3}{2}
\large z_4 = 125\sqrt {5}\left( \Large \frac{1}{2}\large +\Large \frac{\sqrt {3}}{2}\large \text{i}\right) = \Large \frac{125\sqrt {5}}{2}\large +\Large \frac{125\sqrt {15}}{2}\large \text{i}