Question

NEED HELP ! 20 POINTS

Answer 1

If $z=1-i$, then $|z|=\sqrt{1^2+(-1)^2}=\sqrt2$ and $\arg z=-\dfrac\pi4$ because $z$ lies in the fourth quadrant.

By DeMoivre's theorem,

$z=|z|e^{i\arg z}\implies z^{10}=(\sqrt2)^{10}e^{-i10\pi/4}=32e^{-i5\pi/2}=32e^{-i\pi/2}=-32i$

so the answer is B.