- #1

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Say I have a function f(z) = log(z

^{2}- 1). Why is a simple branch cut connecting z = -1 and z = +1 not sufficient to define an analytic function? On the other hand, why is it sufficient for the function f(z) = (z^2 - 1)^(1/2) ?

This is in the complex plane where z = a + ib.