Question

Represent the complex number $Z=1+i\sqrt{3}$ in the polar form.

Answer 1

$Z=1+i\sqrt{3}$

$r=|Z|=\sqrt{(1{)}^2+(\sqrt{3}{)}^2}=2$

$\theta =ta{n}^{-1}|\frac{\sqrt{3}}{1}|=\frac{\pi }{3}$

Polar form is

$=r(cos\theta +isin\theta )=2(cos\frac{\pi }{3}+isin\frac{\pi }{3})$