SOLUTION: Simplify the following and give answers in the form a+bi. (3 cos(pi/8) + 3i sin(pi/8))^4

Algebra ->  Complex Numbers Imaginary Numbers Solvers and Lesson -> SOLUTION: Simplify the following and give answers in the form a+bi. (3 cos(pi/8) + 3i sin(pi/8))^4      Log On


   

Question 220632: Simplify the following and give answers in the form a+bi.
(3 cos(pi/8) + 3i sin(pi/8))^4
Answer by Alan3354(69443) About Me  (Show Source):
You can put this solution on YOUR website!
(3 cos(pi/8) + 3i sin(pi/8))^4
z = (3 cos(pi/8) + 3i sin(pi/8)) = 3cis(pi/8)
z^4 = 81cis(pi/2)
= 81cos(pi/2) + 81isin(pi/2)
= 81i