Question

NEED HELP ! 20 POINTS

Use Demoivres Theorem to find ( 1 - i )^10
a. 32 - 32i
b. -32i
c. -32 + 32i
d. 32

Answer 1

B

Explanation:

edge 2020

Answer 2

If
`z=1-i`, then
`|z|=√(1^2+(-1)^2)=\sqrt2` and
`\arg z=-\frac\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.