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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

Best Answer 

 #1
avatar+105634 
+15

Hi Shades :)

 

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?

 

 

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

.
 Dec 3, 2015
edited by Melody  Dec 3, 2015
edited by Melody  Dec 5, 2015
 #1
avatar+105634 
+15
Best Answer

Hi Shades :)

 

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
avatar+466 
+5

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

 Dec 3, 2015
 #3
avatar+105634 
+5

You are very welcome Shades :)

 

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

https://www.adelaide.edu.au/mathslearning/bridging/resources/MT5ComplexBook_Feb2013.pdf

 Dec 3, 2015
 #4
avatar+104855 
+5

Very nice, Melody !!!

 

 

cool cool cool

 Dec 3, 2015
 #5
avatar+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?

 Dec 4, 2015
 #6
avatar+105634 
0

Thanks Chris . :D

 

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

 Dec 5, 2015

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