Re: Re: ComplexExpand confusion

*To*: mathgroup at smc.vnet.net*Subject*: [mg60158] Re: [mg60135] Re: [mg60109] ComplexExpand confusion*From*: Murray Eisenberg <murray at math.umass.edu>*Date*: Mon, 5 Sep 2005 02:27:51 -0400 (EDT)*Organization*: Mathematics & Statistics, Univ. of Mass./Amherst*References*: <200509040701.DAA07297@smc.vnet.net>*Reply-to*: murray at math.umass.edu*Sender*: owner-wri-mathgroup at wolfram.com

(-1)^(1/4) does not look like polar form to me! Bob Hanlon wrote: > The Further Examples for ComplexExpand states that it will expand complex > powers, i.e., it is converting from the polar form of the complex number to its > Cartesian form. > > (-1)^(1/4)//ComplexExpand > > (1 + I)/Sqrt[2] > > %//FullSimplify > > (-1)^(1/4) > > You get the same result with ExpToTrig > > (-1)^(1/4)//ExpToTrig > > (1 + I)/Sqrt[2] > > > Bob Hanlon > > >>From: mike_in_england2000 at yahoo.co.uk To: mathgroup at smc.vnet.net >>Date: 2005/09/03 Sat AM 02:05:58 EDT >>Subject: [mg60158] [mg60135] [mg60109] ComplexExpand confusion >> >>Hi >> >>The Mathematica help system says that >> >>"ComplexExpand[expr] expands expr assuming that all variables are >>real." >> >>which is fine and explains why expressions such as >>ComplexExpand[Conjugate[x +I y]] work.All seems obvious so far. >> >>What is confusing me though is why does >> >>ComplexExpand[(-1)^(1/4)] >> >>give the result >> >>(1 + I)/Sqrt[2] >> >>I know this the correct result but in the expression (-1)^(1/4) there >>are no variables. The numbers involved are real so what on earth is >>ComplexExpand doing? Is this a stupid question? Should I have drank >>more coffee before posting this. >> >>Thanks >>Mike >> >> > > > -- Murray Eisenberg murray at math.umass.edu Mathematics & Statistics Dept. Lederle Graduate Research Tower phone 413 549-1020 (H) University of Massachusetts 413 545-2859 (W) 710 North Pleasant Street fax 413 545-1801 Amherst, MA 01003-9305

**References**:**Re: ComplexExpand confusion***From:*Bob Hanlon <hanlonr@cox.net>