Как возвести комплекстное число в степень.

z=-2-2i, n=8

z^n = ?

|z|=√ ((-2) ² + (-2) ²) = √ (4+4) = √8=2√2

argz=-π+arctg (-2/-2) = - π-arctg1=-π+π/4=-3π/4

z=2√2 * (cos (-3π/4) + isin (-3π/4))

z^8 = (2√2) ^8 * (cos (-3π/4 * 8) + isin (-3π/4*8)) = 4096 * (cos (-6π) + isin (-6π)) =

=4096 * (cos0+Isin0) = 4096 * (1+i*0) = 4096