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# Complex Numbers

+5
801
6

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?

Dec 3, 2015

#1
+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?

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

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

#1
+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
+5

That's exactly how it is supposed to look at the end. Thank you very much! Dec 3, 2015
#3
+5

You are very welcome Shades :)

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

Dec 3, 2015
#4
+5

Very nice, Melody !!!   Dec 3, 2015
#5
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?

Dec 4, 2015
#6
0

Thanks Chris . :D

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

Dec 5, 2015