Question

Помогите решить задание по математике. 10-11 класс

Answer 1

$\displaystyle\\z=-\sqrt{3}-i\\\\z=r(\cos(\phi)+i\sin(\phi))\\\\\\r=\sqrt{a+b}=\sqrt{(-\sqrt{3})^2+(-1)^2}=\sqrt{3+1}=\sqrt{4}=2\\\\\\\arg(z)=\phi=\pi+\arctan\bigg(\frac{\mid -1 \mid}{\mid -\sqrt{3} \mid}\bigg)=\pi+\arctan\frac{1}{\sqrt{3}}=\pi+\frac{\pi}{6}=\frac{7\pi}{6}\\\\\\ z=r(\cos(\phi)+i\sin(\phi))\\\\\\z=2\bigg(\cos\bigg(\frac{7\pi}{6}\bigg)+i\sin\bigg(\frac{7\pi}{6}\bigg)\bigg)$