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## Homework Statement

Let f(z) denote the multivalued function [itex](z^{2} − 1)^{1/2}[/itex]

.

Deﬁne a branch of f(z) which is analytic in the interior of the unit disk |z| < 1

**2. The attempt at a solution**

Having a bit of trouble getting started.

I have rewritten f(z) as [itex]((z-1)(z+1))^{1/2}[/itex] as per a hint in the question.

Giving me branch points at z=1 and z=-1 and a branch cut between.

I could rewrite each part in terms of polar representation but there I get stuck on defining which argument to take for my branch.

Any help would be much appreciated.