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

Sean A. Irvine sairvin at xtra.co.nz
Fri Aug 6 01:16:46 CEST 2010


(e i)^(pi i) = -(e^(-pi^2/2)), so no.

Sean.

Alonso Del Arte wrote:
> 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?
> 
> Al
> 
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