If trying to find a branch of ##(z^2-1)^{1/2}##, it can be shown that one acceptable answer is: ## i e^{0.5 Log(1-z^2)}##(adsbygoogle = window.adsbygoogle || []).push({});

But I just want to clarify, is not the following an acceptable answer, too: ## iz e^{0.5 Log (\frac{1}{z^2} -1)}##

It appears the argument of Log in both cases is always defined when inside the unit circle. Are they not both valid branches?

(Where Log denotes the principal branch with a cut on the non-positive real axis.)

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# I Finding a branch of a function in the unit disk

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