Question 631743: Please use de Moivre’s Theorem to find [2-2 sqrt (3i)^10]. Write your answer in exact rectangular form. Thanks! Answer by Alan3354(69443) (Show Source):
You can put this solution on YOUR website! [2-2 sqrt (3i)]^10. Write your answer in exact rectangular form.
If you mean [2 - 2sqrt(3)i]^10
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r = sqrt(4 + 12) = 4
tan = -sqrt(3) --> angle = 300 degs
--> 4cis(300)
^10 --> 4^10cis(3000)
= 2^20cis120
= 2^20*(-0.5 + i*sqrt(3)/2)
= 2*19*(-1 + isqrt(3))
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or
-524288 + i*524288*sqrt(3)
