SOLUTION: Apply DeMoivre's Theorem and leave the result in trigonometric form (2 + 2i)^6

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Question 1174588: Apply DeMoivre's Theorem and leave the result in trigonometric form
(2 + 2i)^6




Answer by ikleyn(52794) About Me  (Show Source):
You can put this solution on YOUR website!
.

Notice that  2 + 2i = 2%2Asqrt%282%29%2A%28sqrt%282%29%2F2+%2B+i%2A%28sqrt%282%29%2F2%29%29 = 2%2Asqrt%282%29%2Acis%28pi%2F4%29.


Therefore, according to deMoivre's formula


    %282+%2B+2i%29%5E6 = %282%2Asqrt%282%29%29%5E6%2Acis%286pi%2F4%29 = 2%5E9%2Acis%283pi%2F2%29 = -512*i.     ANSWER