Umocnění komplexního čísla
Umocni komplexní číslo a pak ho převeď do algebraického tvaru:
\large z_4 = \left[ 7\left( \cos {\Large \frac{7\pi}{4}\large }+\text{i}\sin {\Large \frac{7\pi}{4}\large }\right) \right] ^5
\cos\:\frac{3\pi}{4}=\frac{\sqrt2}{2}
\sin\:\frac{3\pi}{4}=-\frac{\sqrt2}{2}
\large z_4 =7^5\cdot \left( \Large \frac{\sqrt {2}}{2}\large -\text{i}\Large \frac{\sqrt {2}}{2}\large \right) =\Large \frac{7^5\sqrt {2}}{2}\large -\Large \frac{7^5\sqrt {2}}{2}\large \text{i}
\cos\:\frac{3\pi}{4}=-\frac{\sqrt2}{2}
\sin\:\frac{3\pi}{4}=\frac{\sqrt2}{2}
\large z_4 =7^5\cdot \left( -\Large \frac{\sqrt {3}}{2}\large +\text{i}\Large \frac{\sqrt {2}}{2}\large \right) =-\Large \frac{7^5\sqrt {3}}{2}\large +\Large \frac{7^5\sqrt {2}}{2}\large \text{i}
\cos\:\frac{3\pi}{4}=-\frac{\sqrt2}{2}
\sin\:\frac{3\pi}{4}=\frac{\sqrt2}{2}
\large z_4 =7^5\cdot \left( -\Large \frac{\sqrt {2}}{2}\large +\text{i}\Large \frac{\sqrt {2}}{2}\large \right) =-\Large \frac{7^5\sqrt {2}}{2}\large +\Large \frac{7^5\sqrt {2}}{2}\large \text{i}
\cos\:\frac{3\pi}{4}=-\frac{\sqrt2}{2}
\sin\:\frac{3\pi}{4}=\frac{\sqrt2}{2}
\large z_4 =7^5\cdot \left( -\Large \frac{\sqrt {2}}{2}\large +\text{i}\Large \frac{\sqrt {3}}{2}\large \right) =-\Large \frac{7^5\sqrt {2}}{2}\large +\Large \frac{7^5\sqrt {3}}{2}\large \text{i}