Question

what is the polar form of -3+sqrt3i

Answer 1

Solution

For this case we have the following number given:

$-3+\sqrt[]{3}i$

We can see that x = -3 and y = - sqrt(3)

The angle is given by:

$\arctan (\frac{-\sqrt[]{3}}{3})=-30=-\frac{\pi}{6}$

The radius would be:

$r=\sqrt[]{(3)^2+(-\sqrt[]{3})^2}=\sqrt[]{12}$

And the polar form would be given by:

$z=\sqrt[]{12}(\cos (-\frac{\pi}{6})+i\sin (-\frac{\pi}{6}))\text{ }$