Question

Represent follow complex no. in polar form.
$z=-1+\sqrt{3}i$

Answer 1

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

$z=r(cos\theta +isin\theta )\to$ polar from

$z=2[-\frac{1}{2}+\frac{\sqrt{3}}{2}i]$

on comparing, $r=2.$

$cos\theta =-1/2\Rightarrow \theta =\frac{2\pi }{3}$

$sin\theta =\frac{\sqrt{3}}{2}\Rightarrow \theta =\frac{\pi }{3}\Rightarrow \frac{2\pi }{3}$

$\therefore \theta =\frac{2\pi }{3}$

$\therefore r=2$ and $\theta =\frac{2\pi }{3}$

$\therefore z=2\left[cos\right(\frac{2\pi }{3})+isin(\frac{2\pi }{3}\left)\right]\to$ polar form.