Re: Re: How to evaluate Exp[I Pi(1+x)]?
- To: mathgroup at smc.vnet.net
- Subject: [mg52833] Re: [mg52770] Re: How to evaluate Exp[I Pi(1+x)]?
- From: Andrzej Kozlowski <akoz at mimuw.edu.pl>
- Date: Tue, 14 Dec 2004 05:59:31 -0500 (EST)
- References: <200412100123.UAA18952@smc.vnet.net> <firstname.lastname@example.org> <200412130922.EAA23340@smc.vnet.net>
- Sender: owner-wri-mathgroup at wolfram.com
This works but for a different reason, which is that the result holds even if you do not assume that x is real (see my latest posting). (If it were necessary that x is real your approach would not work since ComplexExpand would not pass this information to FullSimplify.) On 13 Dec 2004, at 18:22, Dr. Wolfgang Hintze wrote: > I remember that ComplexExpand[expr] assumes parameters in expr to be > real. Hence the following was the shortest succesful expansion I found: > > In:= > FullSimplify[ComplexExpand[E^(I*Pi*(1 + x))]] > > Out= > -E^(I*Pi*x) > > Simplify is not enough. > > By the way, while doing much complex function work recently I devolped > the habit to always use ComplexExpand as the first opration. > Otherwise even the simplest operations Re, Im, Abs don't work. > > Regards, > Wolfgang > > Andrzej Kozlowski wrote: > >> On 10 Dec 2004, at 10:23, hello wrote: >> >> >>> Is there a way to evaluate Exp[I Pi (1+x)]? I am expecting to see the >>> result to be: >>> >>> -Exp[I Pi x] >>> >>> because Exp[I Pi] can be reduced to shorter form. >>> >>> >>> >>> >>> >> >> Hello? >> >> FullSimplify[ComplexExpand[Exp[I*Pi*(1 + x)]], >> x $B":(B Reals] >> >> >> -E^(I*Pi*x) >> >> >> >> Andrzej Kozlowski >> Chiba, Japan >> http://www.akikoz.net/~andrzej/ >> http://www.mimuw.edu.pl/~akoz/ >> >> >