SOLUTION: Find the power and express in rectangular form. {{{(sqrt(2)+i (sqrt(2)))^5}}}

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Question 878302: Find the power and express in rectangular form.
%28sqrt%282%29%2Bi+%28sqrt%282%29%29%29%5E5
Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
sqrt%282%29%2Bi%2A%28sqrt%282%29%29=2%28sqrt%282%29%2F2%2B%28sqrt%282%29%2F2%29i%29
sqrt%282%29%2Bi%2A%28sqrt%282%29%29=2%28cos%2845%29%2Bi%2Asin%2845%29%29
Using DeMoivre's theorem,

%28sqrt%282%29%2Bi%2A%28sqrt%282%29%29%29%5E5=32%28cos%28225%29%2Bi%2Asin%28225%29%29

%28sqrt%282%29%2Bi%2A%28sqrt%282%29%29%29%5E5=-16sqrt%282%29%281%2Bi%29%29
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(-16sqrt%282%29,-16sqrt%282%29)