(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

Given that the standard square root sqrt(anything) has a branch cut from (-inf,0), find the branch cuts of the following:

z+sqrt(z^2-1)

z+isqrt(1-z^2)

z+sqrt(z+1)sqrt(z-1)

2. Relevant equations

3. The attempt at a solution

I understand what branch cuts do (multivalue functions -> single value), I am just having trouble since all three of those expressions can be reduced to the same expression - I don't see why they would need different cuts? I can't really find any examples online and my book only has less than one paragraph explaining branch cuts (let alone examples).

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# Branch cuts in complex analysis

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