Question
Take x=i, where i²=−1. Using the principal complex logarithm to define the power, find xˣ.
The correct answer is
e-π/2
With x=i, the principal logarithm is Log i=iπ/2. Hence \(x^x=\exp(i\operatorname{Log}i)=e^{-\pi/2}\). Other logarithm branches would give different positive real values.
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