SOLUTION: Find the indicated power using De Moivre's Theorem. (Express your fully simplified answer in the form a + bi. (2 − 2i)^7?

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Question 967556: Find the indicated power using De Moivre's Theorem. (Express your fully simplified answer in the form a + bi.
(2 − 2i)^7?
Answer by Alan3354(69443) About Me  (Show Source):
You can put this solution on YOUR website!
Find the indicated power using De Moivre's Theorem. (Express your fully simplified answer in the form a + bi.
(2 - 2i)^7?
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r+=+sqrt%282%5E2+%2B+2%5E2%29+=+sqrt%288%29
--> sqrt(8)cis(315)
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%28sqrt%288%29cis%28315%29%29%5E7+=+%28sqrt%288%29%29%5E7cis%28315%2A7%29
= 8%5E3%2Asqrt%288%29cis%282205%29
= 1024%2Asqrt%282%29cis%2845%29
= 1024sqrt%282%29%2Asqrt%282%29%2F2+=+i%2A1024sqrt%282%29%2Asqrt%282%29%2F2
= 1024 + 1024i