Goniometrický tvar komplexního čísla
Uprav zadané komplexní číslo a pak ho zapiš v goniometrickém tvaru:
\large z_5 = \Large \frac{-\sqrt {3}+3\text{i}}{\frac{\sqrt {3}}{2}\left( \cos {\frac{2\pi}{3}}+\text{i}\sin {\frac{2\pi}{3}}\right) }\large
\frac{z_1}{z_2}=|\frac{z_1}{z_2}|\:\left\lbrack\cos\left(\alpha_1-\alpha_2\right)+\sin\left(\alpha_1-\alpha_2\right)\right\rbrack
\frac{2\sqrt3\:\left(\frac{2\pi}{3}+i\:\sin\:\frac{2\pi}{3}\right)}{\frac{\sqrt3}{2}\left(\cos\:\frac{2\pi}{3}+i\:\sin\frac{2\pi}{3}\right)}
\large =3\left( \cos {0}+\text{i}\sin {0}\right)
\frac{z_1}{z_2}=|\frac{z_1}{z_2}|\:\left\lbrack\cos\left(\alpha_1-\alpha_2\right)+\sin\left(\alpha_1-\alpha_2\right)\right\rbrack
\frac{2\sqrt3\:\left(\frac{2\pi}{3}+i\:\sin\:\frac{2\pi}{3}\right)}{\frac{\sqrt3}{2}\left(\cos\:\frac{2\pi}{3}+i\:\sin\frac{2\pi}{3}\right)}
\large =4\left( \cos {0}+\text{i}\sin {0}\right)
\frac{z_1}{z_2}=|\frac{z_1}{z_2}|\:\left\lbrack\cos\left(\alpha_1-\alpha_2\right)+\sin\left(\alpha_1-\alpha_2\right)\right\rbrack
\frac{2\sqrt3\:\left(\frac{2\pi}{3}+i\:\sin\:\frac{2\pi}{3}\right)}{\frac{\sqrt3}{2}\left(\cos\:\frac{2\pi}{3}+i\:\sin\frac{2\pi}{3}\right)}
\large =4\left( \cos {\pi}+\text{i}\sin {0}\right)
\frac{z_1}{z_2}=|\frac{z_1}{z_2}|\:\left\lbrack\cos\left(\alpha_1+\alpha_2\right)+\sin\left(\alpha_1+\alpha_2\right)\right\rbrack
\frac{2\sqrt3\:\left(\frac{2\pi}{3}+i\:\sin\:\frac{2\pi}{3}\right)}{\frac{\sqrt3}{2}\left(\cos\:\frac{2\pi}{3}+i\:\sin\frac{2\pi}{3}\right)}
\large =4\left( \cos {0}+\text{i}\sin {\pi}\right)