SOLUTION: Simplify (3 – √3 i)^4 and express the result in rectangular form.

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Question 1022517: Simplify (3 – √3 i)^4 and express the result in rectangular form.
Answer by Alan3354(69443) About Me  (Show Source):
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Simplify (3 – i*sqrt(3)^4 and express the result in rectangular form.
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Since it's 4th power, square it twice.
(3 – i*sqrt(3))^2 = 9 - 6i*sqrt(3) + 3i^2 = 6 - 6sqrt(3)i
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Square again:
(6 - 6sqrt(3)i)^2 = 36 - 72*sqrt(3)i + 108i^2
= -72 - i*72*sqrt(3)
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Had the exponent been less convenient DeMoivre's Theorem could be used.