Complex exponentiation

For nonzero complex $z$ and complex $w$, the multivalued power is

The principal cube root is $z^{1/3}=\exp (\mathrm{Log}z/3)$ 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, $z^{1/3}{e}^{\pm i\pi /3}$.

For every integer $n$ and real $\theta$,It converts powers of a complex number in polar form into multiplication of its complex argument.