SOLUTION: Find the polar representation of Z= Cosa+Sina+i(Sina-Cosa) where a<[0, 2&#960;)

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Question 773999: Find the polar representation of Z= Cosa+Sina+i(Sina-Cosa) where a<[0, 2π)
Answer by Edwin McCravy(20056)   (Show Source): You can put this solution on YOUR website!
To find the argument ,



Write  as 



Cross-multiply

 

 

Rearrange the equation:

 

 

  



Divide both sides by 





, 

, 

To find the modulus or absolute value r:







Using the identity cosine² + sine² = 1, the right side is just 2

r² = 2

r = √2 

Polar forms:

√2[cos() + i·sin()]

√2[cos() + i·sin()]

Edwin


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