SOLUTION: How do you write (2 square root of 3) - 2i in polar notation? I keep getting 4(cos 150 + isin 150). However, the answer key in my book says it's 4(cos 330 + isin 330). Help.

Algebra ->  Complex Numbers Imaginary Numbers Solvers and Lesson -> SOLUTION: How do you write (2 square root of 3) - 2i in polar notation? I keep getting 4(cos 150 + isin 150). However, the answer key in my book says it's 4(cos 330 + isin 330). Help.      Log On


   

Question 616169: How do you write (2 square root of 3) - 2i in polar notation? I keep getting 4(cos 150 + isin 150). However, the answer key in my book says it's 4(cos 330 + isin 330). Help.
Answer by stanbon(75887) About Me  (Show Source):
You can put this solution on YOUR website!
How do you write (2 square root of 3) - 2i in polar notation? I keep getting 4(cos 150 + isin 150). However, the answer key in my book says it's 4(cos 330 + isin 330). Help.
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2*sqrt(3) - 2i corresponds to (2sqrt(3),-2) which is in the 4th Quadrant.
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r = sqrt[(2sqrt(3))^2 + 2^2] = sqrt[16] = 4
theta = tan^-1(-2/(2sqrt(3)) = tan^-1(-1/sqrt(3)) = -30 degrees or +330
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Cheers,
Stan H.