1. The problem statement, all variables and given/known data Hi, I'm stuck with this question: How many branches (solutions) and branch points does the function f(z) = (z2 +1 +i)1=4 have? Give an example of a branch of the multi- valued function f that is continuous in the cut-plane, for some choice of branch cut(s). Now by choosing different branch cut(s), provide a different example. 2. Relevant equations f(z) = (z2 +1 +i)1=4 3. The attempt at a solution So I've done the first part, by setting f(z) = 0 then solving for two solutions of z to be sqrt(-1-i) and z= -sqrt(-1-i), but I'm not sure how to proceed onto the next part of the question.