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

Define an analytic branch f(z) of w, such that f(z)=0 for the limit of z->[itex]\infty[/itex]

Now what is f(1)?

2. Relevant equations

[itex]w=\frac{z+i}{z-i}[/itex]

3. The attempt at a solution

The branch cut of the logarithm is: [itex](-\infty,0)[/itex]

All branches of the logarithm are:

f(z)=Log(z)+iArg(z)=Log(z)+2i[itex]\pi[/itex]k

But then f(1)=0, which is wrong.

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# Principal branch of the logarithm

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