You have to know 2 things:

1. How to change from a+bi form to trig form r(cosq + i sinq)

use tanq =  and r = 

2.  How to raise a complex number in trig form using DeMoivre's
   formula:

[r(cosq + i sinq)]n = rn[cos(nq) + i·sin(nq)]


(2+2squareroot3i)^6


1. To change from 2+2i form to trig form r(cosq + i·sinq)

use tanq =  = 
therefore q = 60°

and r =  =  =  =  = 4

So 2 + 2i = 4(cos60° + i·sin60°) 


2. To raise this complex number in trig form using DeMoivre's
   formula:

[4(cos60° + i·sin60°)]6 = 46[cos(6·60°) + i·sin(6·60)] =
4096(cos360° + i·sin360°) = 4096(cos0° + i·sin0°) = 
4096(1+i·0) = 4096(1+0) = 4096(1) = 4096.

answer: 4096.

Edwin