SOLUTION: express ( -1 + root(3)i)^10 in a+bi form

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Question 642901: express ( -1 + root(3)i)^10 in a+bi form
Answer by Alan3354(69443) About Me  (Show Source):
You can put this solution on YOUR website!
express ( -1 + root(3)i)^10 in a+bi form
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%28-1+%2B+sqrt%283%29i%29%5E10
is in a + bi form, with the exponent.
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If you want to simplify it some:
magnitude (z) = sqrt%281+%2B+3%29+=+2
---> 2cis(atan(-sqrt(3))
z = 2cis(300)
z^10 = 2^10cis(3000)
= 1024cis(120)
= 1024cos(120) + 1024i*sin(120)
= -512+%2B+512sqrt%283%29i