Question:if $z=-1-i$ then what is $z^8$

Question

For the question if $z=-1-i$ then what is $z^8$? The correct answer is $32e^{10πi}$ which doesn't make sense since I am getting $16e^{10πi}$.

Answer 1

The correct answer is "none of the above."

$(-1-i)^2=2i$, so $(-1-i)^8=(2i)^4=2^4i^4=16.$

(This agrees with the answer you wrote, because $e^{10\pi i}=(e^{2\pi i})^5=1.$)