Branch points [Complex Analysis]

[machofan]

Homework Statement

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.

Homework Equations

f(z) = (z2 +1 +i)1=4

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. [/B]

 

[haruspex]

(z2 +1 +i)1

What does that expression mean? It looks like maybe z²+1+i, but what is the final 1 doing?

 

[machofan]

Woops sorry! The function z is meant to say (z^2+1+i)^1/4