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^{{2ii\pi }}\,

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


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