Question

z= -2 + 2i find z^24 using de moivre's theorem

Answer 1

do you recall what \(-2+2i\) is in polar form?

Answer 2

yes

Answer 3

multiply the angle by 24, raise \(2\sqrt{2}\) to the power of 24, which is a ridiculously large number

Answer 4

is that it?

Answer 5

yes

Answer 6

oh thats easy thank you again!

Answer 7

well you might want to change the angle

Answer 8

change it to what?

Answer 9

\[\frac{3\pi}{4}\times 24=18\pi\]

Answer 10

and \(18\pi\) is conterminal with 0
so you might want to write
\[(2\sqrt{2})^{24}\left(\cos(0)+i\sin(0)\right)\]

Answer 11

okay