# What is the trigonometric form of  (4-4i) ?

Mar 15, 2016

$= 4 \sqrt{2} \left[\cos \left(- \frac{3 \pi}{4}\right) + i \sin \left(- \frac{3 \pi}{4}\right)\right]$

#### Explanation:

The trigonometric form looks like this : $r \left(\cos \theta + i \sin \theta\right)$

where $r$ is the modulus and $\theta$ the arguement.

Step 1:
find the modulus(magnitude)
$r = \sqrt{{\left(4\right)}^{2} + {\left(- 4\right)}^{2}} = 4 \sqrt{2}$

Step 2:
find the arguement.
$\theta = \arctan \left(\frac{4}{4}\right) - \pi = \frac{\pi}{4} - \pi = - \frac{3 \pi}{4}$

Step 3:
$z = 4 \sqrt{2} \left[\cos \left(- \frac{3 \pi}{4}\right) + i \sin \left(- \frac{3 \pi}{4}\right)\right]$