# How do you write the following in trigonometric form and perform the operation given 4(1-sqrt3i)?

Oct 28, 2016

The trigonometric form is $z = 8 \left(\cos \left(- \frac{\pi}{3}\right) + i \sin \left(- \frac{\pi}{3}\right)\right)$

#### Explanation:

let $z = 4 \left(1 - i \sqrt{3}\right)$
The trigonometric form is $z = r \left(\cos \theta + i \sin \theta\right)$
Rewriting $z = 8 \left(\frac{1}{2} - \frac{i \sqrt{3}}{2}\right)$

Comparing this to the first equation
$\cos \theta = \frac{1}{2}$ and $\sin \theta = - \frac{\sqrt{3}}{2}$
So we are in the 4th quadrant
and $\theta = - \frac{\pi}{3}$

So the trigonometric form is $z = 8 \left(\cos \left(- \frac{\pi}{3}\right) + i \sin \left(- \frac{\pi}{3}\right)\right)$