Math Help - Solve for z

1. Solve for z

Solve z^6 + 8 = 0 for z.

I assume that there are "6 6th roots of unity"?

2. Hello, Ideasman!

Solve: . $z^6 + 8 \:= \:0$

We have: . $z^6 \;=\;-8 \;=\;8\bigg[\cos\left(\pi + 2\pi n\right) + i\sin\left(\pi + 2\pi n\right)\bigg]$

Hence: . $z \;=\;(2^3)^{\frac{1}{6}}\bigg[\cos(\pi + 2\pi n) + i\sin(\pi + 2\pi n)\bigg]^{\frac{1}{6}}$

. . . . . . $z \;=\;\sqrt{2}\bigg[\cos\left(\frac{\pi}{6} + \frac{\pi}{3}n\right) + i\sin\left(\frac{\pi}{6} + \frac{\pi}{3}n\right)\bigg]$

Then let $n \:=\:0,1,2,3,4,5$