# How do you divide  (6+4i)/(1-i)  in trigonometric form?

Mar 30, 2016

$\sqrt{26} c i s 1.373$

#### Explanation:

Please note this answer will work in radians, and to 4s.f, and will shorten $\cos \theta + i \sin \theta$ to $c i s \theta$
.
First convert to polar form.
This yields (sqrt52cis0.5880)/(sqrt2cis(-pi/4)

Note that $\frac{{r}_{2} c i s {\theta}_{2}}{{r}_{1} c i s {\theta}_{1}} = {r}_{2} / {r}_{1} c i s \left({\theta}_{2} - {\theta}_{1}\right)$

Thus $\frac{\sqrt{52} c i s 0.5880}{\sqrt{2} c i s \left(\frac{\pi}{4}\right)} = \frac{\sqrt{52}}{\sqrt{2}} c i s \left(0.5880 + \frac{\pi}{4}\right) = \sqrt{26} c i s 1.373$