# How do you write the complex number in trigonometric form 3-3i?

May 5, 2018

In the trigonometric form we will have: $3 \sqrt{2} \left(\cos \left(- \frac{\pi}{4}\right) + i \sin \left(- \frac{\pi}{4}\right)\right)$

#### Explanation:

We have
3-3i
Taking out 3 as common we have 3(1-i)
Now multiplying and diving by $\sqrt{2}$ we get, 3 $\sqrt{2}$(1/ $\sqrt{2}$- i/ $\sqrt{2}$)

Now we have to find the argument of the given complex number which is tan(1/$\sqrt{2}$/(-1/$\sqrt{2}$)) whixh comes out to be -$\pi$/4 .Since the sin part is negative but cos part is positive so it lies in quadrant 4, implying that argument is $- \frac{\pi}{4}$.
Hence
$3 \sqrt{2} \left(\cos \left(- \frac{\pi}{4}\right) + i \sin \left(- \frac{\pi}{4}\right)\right)$ is the answer.

Hope it helps!!