CVEL7

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Evaluate $(-1)^{2i}\,$ on the principal branch.

$(-1)^{2i} = e^{2i\mathrm{Log}(-1)}\,$

And

$\mathrm{Log}(-1) = \mathrm{Log}|-1| + i \mathrm{Arg}(-1)\,$

$= \mathrm{Log}(1) + i\pi\,$

$= i\pi\,$

So

$(-1)^{2i} = e^{2i i\pi} \,$

$= e^{-2\pi}\,$

Main Page : Complex Variables : Exponential and Log

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