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Evaluate $\displaystyle(-1)^z,\ \text{Re}(z)>-1$

and $(-1)^b,\ b\in \mathbb{R},\ b>-1$

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closed as not a real question by Asaf Karagila, Did, Davide Giraudo, Alexander Gruber, Thomas Feb 21 '13 at 13:25

It's difficult to tell what is being asked here. This question is ambiguous, vague, incomplete, overly broad, or rhetorical and cannot be reasonably answered in its current form. For help clarifying this question so that it can be reopened, visit the help center.If this question can be reworded to fit the rules in the help center, please edit the question.

What's the question? –  Asaf Karagila Feb 21 '13 at 11:38

1 Answer 1

The number $a^b$ is defined as $\exp(b\log a)$, but since $\log a$ is not uniquely determined, neither is $a^b$ (in general). To get a specific value, you need to choose a branch of the complex logarithm.

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