SOLUTION: Find the indicated power of the complex number; (2(cos(pi\3)+isin(pi\3))^5 The slashes are backwards because the slash key doesn't work on this laptop. I've solved the problem dow

Algebra ->  Complex Numbers Imaginary Numbers Solvers and Lesson -> SOLUTION: Find the indicated power of the complex number; (2(cos(pi\3)+isin(pi\3))^5 The slashes are backwards because the slash key doesn't work on this laptop. I've solved the problem dow      Log On


   

Question 970003: Find the indicated power of the complex number; (2(cos(pi\3)+isin(pi\3))^5
The slashes are backwards because the slash key doesn't work on this laptop. I've solved the problem down the best I could, but I just couldn't get one of the answers. I got 32(0+i), and couldn't move any farther. It didn't match any of the multiple choice on my homework.
Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
Using DeMoivre's theorem,

%282%28cos%28pi%2F3%29%2Bisin%28pi%2F3%29%29%29%5E5=32%281%2F2-i%28sqrt%283%29%2F2%29%29
%282%28cos%28pi%2F3%29%2Bisin%28pi%2F3%29%29%29%5E5=16-%2816sqrt%283%29%29i