Principal cube root
= Principal cube root
{title2=$z^{1/3}$}
The principal cube root is $z^{1/3}=\exp(\operatorname{Log}z/3)$ using the <principal complex logarithm>. In the right half-plane, its <complex argument> lies between $-\pi/6$ and $\pi/6$. Consequently the roots of $r^3=-z$ consist of one root with negative <real part>, $-z^{1/3}$, and two with positive <real part>, $z^{1/3}e^{\pm i\pi/3}$.