SOLUTION: Simplify (1-(sqrt3)i)^5 (written exactly like that) and express in rectangular form.

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Question 1021336: Simplify (1-(sqrt3)i)^5 (written exactly like that) and express in rectangular form.
Answer by robertb(5830) About Me  (Show Source):
You can put this solution on YOUR website!

=32%28cos+%285pi%2F3%29%2Bsin%285pi%2F3%29i%29%5E5+=+32%28e%5E%28i%285pi%2F3%29%29%29%5E5
=32e%5E%28i%2825pi%2F3%29%29+=+32e%5E%28i8pi%29+e%5E%28i%28pi%2F3%29%29
Now e%5E%28i8pi%29+=+1.
==> 32e%5E%28i8pi%29+e%5E%28i%28pi%2F3%29%29+=+32+e%5E%28i%28pi%2F3%29%29
=32%28cos%28pi%2F3%29+%2B+isin%28pi%2F3%29%29
=32%281%2F2+%2B%28sqrt%283%29%2F2%29i%29
=16+%2B16sqrt%283%29i