Question 1138390
<br>
|z| = {{{sqrt(2^2+2^2) = sqrt(8) = 2*sqrt(2)}}}<br>
theta = 225 degrees = 5pi/4<br>
According to deMoivre's Theorem,<br>
|z^6| = {{{(2*sqrt(2))^6 = 512}}}
theta = 6*5pi/4 = 30pi/4 = 15pi/2 = 3pi/2<br>
So {{{z^6 = -512i}}}