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Homework Statement
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)?
Homework Equations
[itex]w=\frac{z+i}{z-i}[/itex]
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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