SOLUTION: Find the indicated power using De Moivre's Theorem. (Express your fully simplified answer in the form a + bi.) (3 + sqrt 3i)^4

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Question 679687: Find the indicated power using De Moivre's Theorem. (Express your fully simplified answer in the form
a + bi.)
(3 + sqrt 3i)^4
Answer by Alan3354(69443) About Me  (Show Source):
You can put this solution on YOUR website!
(3 + sqrt 3i)^4
--------
z+=+%283+%2B+sqrt%283%29i%29
Mag = 2sqrt(3)
Angle = asin(sqrt(3)/(2sqrt(3)) = asin(1/2)
Angle = 30 degs
z = 2sqrt(3)cis(30)
-------
z^4 = 144cis(120)
= 144*-0.5 + 144i*sqrt(3)/2
= -72 + (72*sqrt(3))i