Goniometrický tvar komplexního čísla
Uprav zadané komplexní číslo a pak ho zapiš v goniometrickém tvaru:
\large z_6 = \Large \frac{\cos {\left( -\frac{\pi}{4}\right) }+\text{i}\sin {\left( -\frac{\pi}{4}\right) }}{-2+2\text{i}}\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{\cos\left(-\frac{\pi}{4}\right)+i\:\sin\left(-\frac{\pi}{4}\right)}{2\sqrt2\left(\cos\:\frac{3\pi}{4}+i\:\sin\:\frac{3\pi}{4}\right)}
\large =\Large \frac{\sqrt {2}}{4}\large \left( \cos {\pi}+\text{i}\sin {\pi}\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{\cos\left(-\frac{\pi}{4}\right)+i\:\sin\left(-\frac{\pi}{4}\right)}{2\sqrt2\left(\cos\:\frac{\pi}{4}+i\:\sin\:\frac{\pi}{4}\right)}
\large =\Large \frac{\sqrt {2}}{4}\large \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{\cos\left(-\frac{\pi}{4}\right)+i\:\sin\left(-\frac{\pi}{4}\right)}{2\sqrt2\left(\cos\:\frac{3\pi}{4}+i\:\sin\:\frac{3\pi}{4}\right)}
\large =\Large \frac{\sqrt {2}}{4}\large \left( \cos {\frac{\pi}{2}}+\text{i}\sin {\frac{\pi}{2}}\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{\cos\left(-\frac{\pi}{4}\right)+i\:\sin\left(-\frac{\pi}{4}\right)}{2\sqrt2\left(\cos\:\frac{3\pi}{4}+i\:\sin\:\frac{3\pi}{4}\right)}
\large =\Large \frac{\sqrt {2}}{4}\large \left( \cos {\frac{3\pi}{2}}+\text{i}\sin {\frac{3\pi}{2}}\right)