+0

# Complex Numbers

+5
430
6
+466

Multiply (6 cis 300o)(2 cis 30o) and express the answer in rectangular form.

I know how to express this in polar form, but how do I put it into rectangular form?

#1
+92206
+15

Multiply (6 cis 300o)(2 cis 30o) and express the answer in rectangular form. {nl} {nl} I know how to express this in polar form, but how do I put it into rectangular form?

$$(6 e^{300^{0}i})*(2e^{30^0i})\\~\\ =12e^{330^0i}\\~\\ =12(cos330+isin330)\\~\\ =12(cos30-isin30))\\~\\ =12(\frac{\sqrt3}{2}-i*\frac{1}{2})\\~\\ =6\sqrt3-6i$$

Melody  Dec 3, 2015
edited by Melody  Dec 3, 2015
edited by Melody  Dec 5, 2015
Sort:

#1
+92206
+15

Multiply (6 cis 300o)(2 cis 30o) and express the answer in rectangular form. {nl} {nl} I know how to express this in polar form, but how do I put it into rectangular form?

$$(6 e^{300^{0}i})*(2e^{30^0i})\\~\\ =12e^{330^0i}\\~\\ =12(cos330+isin330)\\~\\ =12(cos30-isin30))\\~\\ =12(\frac{\sqrt3}{2}-i*\frac{1}{2})\\~\\ =6\sqrt3-6i$$

Melody  Dec 3, 2015
edited by Melody  Dec 3, 2015
edited by Melody  Dec 5, 2015
#2
+466
+5

That's exactly how it is supposed to look at the end. Thank you very much!

#3
+92206
+5

You are very welcome Shades :)

You probably already have a good text book but I found this online.  Maybe it will be helpful.

Melody  Dec 3, 2015
#4
+85726
+5

Very nice, Melody !!!

CPhill  Dec 3, 2015
#5
+466
0

A quick question, why are we simplifying the angles to 30o instead of 60o? 330o is 600 more than 270o so wouldn't the angles be simplified to 60o?

#6
+92206
0

Thanks Chris . :D

I have answered Shades's  last question  - he must have posted it somewhere else :/

Melody  Dec 5, 2015

### 30 Online Users

We use cookies to personalise content and ads, to provide social media features and to analyse our traffic. We also share information about your use of our site with our social media, advertising and analytics partners.  See details