Question 226457
(-1, -sq root 3) ----> *[Tex \LARGE x=-1], *[Tex \LARGE y=-\sqrt{3}]


*[Tex \LARGE r=\|z\|=\sqrt{x^2+y^2}=\sqrt{(-1)^2+\left(-\sqrt{3}\right)^2}=\sqrt{1+3}=\sqrt{4}=2]....*[Tex \LARGE r=2]



*[Tex \LARGE \theta=\tan^{-1}\left(\frac{y}{x}\right)=\tan^{-1}\left(\frac{-\sqrt{3}}{-1}\right)=\tan^{-1}(\sqrt{3})=\frac{\pi}{3}+\pi=\frac{4\pi}{3}]


Answer: polar point is *[Tex \LARGE \left(2, \frac{4\pi}{3}\right)]