All complex sixth roots of 64

Solve $x^6=64$ over the complex numbers, listing all six solutions.

$x=2e^{ik\pi/3}$, $k=0,\dots,5$: that is $\pm2$, $1\pm i\sqrt3$ and $-1\pm i\sqrt3$. Write $64=2^6e^{2\pi ik}$ and take sixth roots; the roots are evenly spaced at $60^\circ$ on the circle of radius $2$.