Goniometrický tvar komplexního čísla
Uprav zadané komplexní číslo a pak ho zapiš v goniometrickém tvaru:
\large z_1 = 2\left( \cos {\pi}+\text{i}\sin {\pi}\right) \cdot \Large \frac{1+\text{i}}{2}\large
z_1\cdot z_2=|z_1|\cdot|z_2|\:\left\lbrack\cos\:\left(\alpha_1+\alpha_2\right)+i\:\sin\left(\alpha_1+\alpha_2\right)\right\rbrack
2\left(\cos\pi+i\:\sin\pi\right)\cdot\frac{\sqrt2}{2}\left(\cos\:\frac{\pi}{4}+i\:\sin\:\frac{\pi}{4}\right)
\large =\sqrt {2}\left( \cos {\Large \frac{5\pi}{4}\large }+\text{i}\sin {\Large \frac{5\pi}{4}\large }\right)
z_1\cdot z_2=|z_1|\cdot|z_2|\:\left\lbrack\cos\:\left(\alpha_1+\alpha_2\right)+i\:\sin\left(\alpha_1+\alpha_2\right)\right\rbrack
2\left(\cos\pi+i\:\sin\pi\right)\cdot\frac{\sqrt2}{2}\left(\cos\:\frac{\pi}{4}+i\:\sin\:\frac{\pi}{4}\right)
\large =\sqrt {2}\left( \cos {\Large \frac{3\pi}{4}\large }+\text{i}\sin {\Large \frac{3\pi}{4}\large }\right)
z_1\cdot z_2=|z_1|\cdot|z_2|\:\left\lbrack\cos\:\left(\alpha_1+\alpha_2\right)+i\:\sin\left(\alpha_1+\alpha_2\right)\right\rbrack
2\left(\cos\pi+i\:\sin\pi\right)\cdot\frac{\sqrt2}{2}\left(\cos\:\frac{\pi}{3}+i\:\sin\:\frac{\pi}{3}\right)
\large =\sqrt {2}\left( \cos {\Large \frac{7\pi}{4}\large }+\text{i}\sin {\Large \frac{7\pi}{4}\large }\right)
z_1\cdot z_2=|z_1|\cdot|z_2|\:\left\lbrack\cos\:\left(\alpha_1+\alpha_2\right)+i\:\sin\left(\alpha_1+\alpha_2\right)\right\rbrack
2\left(\cos\pi+i\:\sin\pi\right)\cdot\frac{\sqrt3}{2}\left(\cos\:\frac{\pi}{4}+i\:\sin\:\frac{\pi}{4}\right)
\large =\sqrt {3}\left( \cos {\Large \frac{5\pi}{4}\large }+\text{i}\sin {\Large \frac{5\pi}{4}\large }\right)