A branch point of is a point which cannot be encircled by a curve such that is single valued and continuous.
Ex has branchpoints at and .
A branch cut is a line that we exclude from our domain.
Let have some branchpoints. A complete branch cut of is a set of cuts s.t. every branchpoint has a cut ending in it; both ends of each cut end on a branch point; any curve in that doesn’t intersect the branch cut encloses either all or none of the branchpoints.