[seqfan] Does (e i)^(pi i) have an imaginary part?

Alonso Del Arte alonso.delarte at gmail.com
Fri Aug 6 00:34:11 CEST 2010

This may be a question with a very obvious response, but it seems to be a
bit over my head. We all know e^(pi i) has no imaginary part (its real part
famously being -1). What about (e i)^(pi i)?

In Mathematica, I get a real part of
approx. -0.007191883355826365607801366396371202955362318 and an imaginary
part of 0. * 10^(-23) (if I ask for 20 decimal places precision) or 0. *
10^(-53) (if I ask for 50). Is the imaginary part so small it's beyond
machine precision, or am I chasing a phantom?


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