use Demoivre's Theorem to find the indicated power of the complex number. Express the result in standard form.

Question

(2+2i)^6

a=2 b=2 n=6

r=sqrt 2^2 + 2^2 = sqrt8
Q=7pi/4

(sqrt8)^6 = 512
512(cos 6/1 x 7pi/4) + i sin 6 x 7pi/4
512 (cos 21pi/2) + i sin (21pi/2)
512(cos pi/2) + i (sin pi/2)
512(2+2i)

1024 + 1024i

Is this correct?