SOLUTION: Find the indicated power using De Moivre's Theorem. (Express your fully simplified answer in the form a + bi. (3sqrt 3 + 3i)^5 ----------- {{{r = sqrt((ssqrt(3))^2 + 3^2) =

Algebra ->  Finance -> SOLUTION: Find the indicated power using De Moivre's Theorem. (Express your fully simplified answer in the form a + bi. (3sqrt 3 + 3i)^5 ----------- {{{r = sqrt((ssqrt(3))^2 + 3^2) =       Log On


   

Question 967689: Find the indicated power using De Moivre's Theorem. (Express your fully simplified answer in the form
a + bi.
(3sqrt 3 + 3i)^5
-----------
r+=+sqrt%28%28ssqrt%283%29%29%5E2+%2B+3%5E2%29+=+sqrt%2827%2B9%29+=+6
Angle = atan(sqrt(3)/3) = 30 degrees
--> %286cis%2830%29%29%5E5
= 7776cis(150)
= 7776%2A%28cos%28150%29+%2B+i%2Asin%28150%29
= -3338%2Asqrt%283%29+%2B+3338i

Answer by Alan3354(69443) About Me  (Show Source):
You can put this solution on YOUR website!
(3sqrt 3 + 3i)^5
-----------
r+=+sqrt%28%28ssqrt%283%29%29%5E2+%2B+3%5E2%29+=+sqrt%2827%2B9%29+=+6
Angle = atan(sqrt(3)/3) = 30 degrees
--> %286cis%2830%29%29%5E5
= 7776*cis(150)
= 7776%2A%28cos%28150%29+%2B+i%2Asin%28150%29%29
= -3338%2Asqrt%283%29+%2B+3338i