Решебник по алгебре и начала математического анализа 11 класс Колягин Задание 666

\[1)\ z = - 4 + 4i\]

\[|z| = \sqrt{( - 4)^{2} + 4^{2}} =\]

\[= \sqrt{16 + 16} = 4\sqrt{2};\]

\[tg\ \varphi = \frac{4}{- 4} = - 1;\]

\[\varphi = \pi + arctg( - 1) =\]

\[= \pi - \frac{\pi}{4} = \frac{3\pi}{4};\]

\[z = 4\sqrt{2}\left( \cos\frac{3\pi}{4} + i\sin\frac{3\pi}{4} \right).\]

\[2)\ z = - \sqrt{3} - i\]

\[|z| = \sqrt{\left( - \sqrt{3} \right)^{2} + ( - 1)^{2}} =\]

\[= \sqrt{3 + 1} = 2;\]

\[tg\ \varphi = \frac{- 1}{- \sqrt{3}} = \frac{1}{\sqrt{3}};\]

\[\varphi = \pi + arctg\frac{1}{\sqrt{3}} = \pi + \frac{\pi}{6} = \frac{7\pi}{6}.\]

\[z = 2\left( \cos\frac{7\pi}{6} + i\sin\frac{7\pi}{6} \right);\]