Riemann surface of $z^{1/n}$: $n$ sheets cyclically connected along the branch cut
The function z^(1/n) is multi-valued in the complex plane: each nonzero z has n distinct nth roots. To define a single-valued branch, one introduces a branch cut, typically along the negative real axis. This visualization shows the n sheets of the Riemann surface for z^(1/n), which are connected along the branch cut in a cyclic pattern. The Riemann surface resolves the multi-valuedness by providing a domain on which the function becomes single-valued and holomorphic.
Controls: Click and drag to orbit, scroll to zoom.
