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

[zak seidov]

In Mathematica,

In[4]:=
Im[(E*I)^(Pi I)]//Simplify

Out[4]=
0

Zak


--- On Thu, 8/5/10, Alonso Del Arte <alonso.delarte at gmail.com> wrote:

> From: Alonso Del Arte <alonso.delarte at gmail.com>
> Subject: [seqfan]  Does (e i)^(pi i) have an imaginary part?
> To: "Sequence Fanatics Discussion list" <seqfan at list.seqfan.eu>
> Date: Thursday, August 5, 2010, 6:34 PM
> 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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