How to find (-2+2i)^16 using DeMoivre's Theorem?

Question

Answer is suppose to be: 2^24 Cis(0)

but I got some crazy: 16777216 cis (2160)

So, I'm messing up somewhere while trying to find theta. Since 2^24 is same as 16777216.

Answer 1

|| -2 + 2i || = 2√2

θ = 3π/4

(2√2)¹⁶ (cos 12π + i sin 12π)

(2¹⁶)(2⁸) (cos 0 + i sin 0)

2²⁴