So \( z^3 = \omega \) or \( z^3 = \omega^2 \), where \( \omega = e^2\pi i/3 = -\frac12 + i\frac{\sqrt3}2 \), and \( \omega^2 = e^-2\pi i/3 = -\frac12 - i\frac{\sqrt3}2 \), both primitive cube roots of unity. - Dyverse