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

[zak seidov]

Because I guess 

(e i)^(pi i) is a slightly more complex case and 

Mathematica needs Simplify to reduce it.

In even more comlex cases you need FullSimplify!

Zak 


--- On Fri, 8/6/10, Alonso Del Arte <alonso.delarte at gmail.com> wrote:

> From: Alonso Del Arte <alonso.delarte at gmail.com>
> Subject: [seqfan] Re: Does (e i)^(pi i) have an imaginary part?
> To: "Sequence Fanatics Discussion list" <seqfan at list.seqfan.eu>
> Date: Friday, August 6, 2010, 1:56 AM
> Thank you very much for the
> explanations. I've worried that my knowledge of
> calculus and trigonometry is sorely lacking, but I see I
> really need to
> brush up on logarithms.
> 
> And thanks to Zak for reminding me of the Im and Simplify
> functions. But it
> leaves me wondering, why exactly is simplification
> necessary here? After
> all, Im[E^(Pi I)] returns 0 without having to ask for a
> Simplify.
> 
> Al
> 
> On Thu, Aug 5, 2010 at 10:55 PM, zak seidov <zakseidov at yahoo.com>
> wrote:
> 
> > 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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> >
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