Liczby zespolone w postaci algebraicznej i trygonometrycznej | math4u.vsb.cz

$\frac{2\left(\cos\frac{5\pi}{12}+\mathrm{i}\sin\frac{5\pi}{12}\right)}{-1-\mathrm{i}}$

$(1-\mathrm{i})^8$

$\frac{-\frac{\sqrt3}{2}-\frac12\mathrm{i}}{{2\mathrm{i}}}\cdot\frac{\mathrm{i}-1}{\cos{\frac{5\pi}{3}}+\mathrm{i}\sin{\frac{5\pi}{3}}}$

$\frac{\cos\frac{2\pi}{3}+\mathrm{i}\sin\frac{2\pi}{3}}{\sqrt{3}-\mathrm{i}}$

$\frac{\cos{\frac{7\pi}{6}}+\mathrm{i}\sin{\frac{7\pi}{6}}}{{2\mathrm{i}}}\cdot\frac{\mathrm{i}-1}{\cos{\frac{5\pi}{3}}+\mathrm{i}\sin{\frac{5\pi}{3}}}$

$\frac{5+3\mathrm{i}}{\mathrm{i}(2\mathrm{i}+\mathrm{i}^2)+\mathrm{i}}$

$(5+2\mathrm{i})(1-\mathrm{i})-\mathrm{i}(2+\mathrm{i})$

$|z-1-2\mathrm i|\geq |z+2-5\mathrm i| $

$\frac{10+5\mathrm{i}}{3+4\mathrm{i}}$

2010013113

Część:

B

Znajdź postać trygonometryczną liczby przeciwnej do liczby \(z=-\frac{\sqrt5}{2} + \mathrm{i}\frac{\sqrt{15}}{2}\).

\(\sqrt{5}\left (\cos \left(-\frac{\pi} {3}\right) + \mathrm{i}\sin \left(-\frac{\pi} {3}\right )\right)\)

\(\sqrt{5}\left (\cos \frac{2\pi } {3} + \mathrm{i}\sin \frac{2\pi } {3}\right )\)

\(\sqrt{10}\left (\cos \frac{5\pi } {3} + \mathrm{i}\sin \frac{5\pi } {3}\right )\)

\(\sqrt{5}\left (\cos \frac{\pi } {3} + \mathrm{i}\sin \frac{\pi } {3}\right )\)