How does one deal with finding the branches & branch cuts of a multi-valued function of a complex variable that is itself the sum of two multi-valued functions, something like the following:(adsbygoogle = window.adsbygoogle || []).push({});

[tex]f(z) = \sqrt{z} + \sqrt{1 - z}[/tex]

[tex]f(z) = \sqrt{z} + \sqrt{z - 1}[/tex]

[tex]f(z) = \sqrt{z} + \sqrt{z(z - 1)}[/tex]

[tex]f(z) = log(z - 1) + \sqrt{z}[/tex]

In other words: how does one understand the algebra of branch cuts and branch points, i.e. the branch cut of a sum is the sum of the branch cuts or whatever the rule is, in general? It really would be fantastic if someone could help me out with this, I have no idea myself & can't find it discussed anywhere.

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# Algebra of Branch Cuts

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