# How do you write the trigonometric form in complex form 6(cos((5pi)/6)+isin((5pi)/6)))?

Oct 29, 2016

THe complex form is $- 3 \sqrt{3} + 3 i$

#### Explanation:

The trigonometric form is $z = r \left(\cos \theta + i \sin \theta\right)$
The complex form is $z = a + i b$
so we have to put the values of $\cos \theta$ and $\sin \theta$
$\cos \left(\frac{5 \pi}{6}\right) = - \cos \left(\frac{\pi}{6}\right) = - \frac{\sqrt{3}}{2}$
and $\sin \left(\frac{5 \pi}{6}\right) = \sin \left(\frac{\pi}{6}\right) = \frac{1}{2}$

So we have $z = 6 \left(\left(- \frac{\sqrt{3}}{2}\right) + \frac{i}{2}\right) = - 3 \sqrt{3} + 3 i$