Root of a complex number
= Root of a complex number
{title2=$w^n=z$}
= Roots of a complex number
{synonym}
For $z=re^{i\theta}\ne0$ and a positive integer $n$, all solutions of $w^n=z$ are $r^{1/n}e^{i(\theta+2\pi k)/n}$ for $k=0,\ldots,n-1$. They differ by multiplication by <roots of unity> and are distinct. If $z=0$, the sole root is zero.