Question

Express the following complex number in polar form and exponential form :
$-1-\sqrt{3}i$

Answer 1

Given,

$z=-1-\sqrt{3}i$

$r=\sqrt{(-1{)}^2+(-\sqrt{3}{)}^2}\Rightarrow r=2$

$\theta ={\tan }^{-1}\left(\frac{-\sqrt{3}}{-1}\right)\Rightarrow \theta =\frac{\pi }{3}$

Polar form $z=r(\cos \theta +i\sin \theta )=2(\cos \frac{\pi }{3}+i\sin \frac{\pi }{3})$

Exponential form $z=r{e}^{i\theta }=2e^{i\frac{\pi }{3}}$