Re: Trouble computing conjugates

*To*: mathgroup at smc.vnet.net*Subject*: [mg88556] Re: [mg88515] Trouble computing conjugates*From*: Murray Eisenberg <murray at math.umass.edu>*Date*: Thu, 8 May 2008 04:14:36 -0400 (EDT)*Organization*: Mathematics & Statistics, Univ. of Mass./Amherst*References*: <200805071107.HAA15027@smc.vnet.net>*Reply-to*: murray at math.umass.edu

ComplexExpand is your friend! It automatically assumes that symbolic quantities within it are real. So: ComplexExpand[Conjugate[c1 u1 + c2 u2]] c1*f + c2*f - I*(c1*g - c2*g) Roy wrote: > I'm having trouble getting mathematica to compute complex conjugates > of some fairly simple expressions: > > If I type the following: > > $Assumptions = {g \[Element] Reals, f \[Element] Reals} > u1 = f + \[ImaginaryI] g > u2 = f - \[ImaginaryI] g > > Then the command: > > Refine[Conjugate [c1 u1]] > > returns: > > f - \[ImaginaryI] g) Conjugate[c1] > > and the command: > > Refine[Conjugate[c1 u1 + u2]] > > returns: > > f + \[ImaginaryI] g + (f - \[ImaginaryI] g) Conjugate[c1] > > as I would expect. But the command: > > Refine[Conjugate[c1 u1 + c2 u2]] > > returns: > > Conjugate[c2 (f - \[ImaginaryI] g) + c1 (f + \[ImaginaryI] g)] > > i.e. it refuses to distribute the complex conjugate throughout the > expression. What I would like it to tell me is: > > (f + \[ImaginaryI] g) Conjugate[c2] + (f - \[ImaginaryI] g) > Conjugate[c1] > > The closest I have been able to come to getting what I want is by > using: > > ComplexExpand[Refine[Conjugate[ c1 u1 + c2 u2]], {c1, c2}] > > but this separates c1 and c2 into their real and imaginary parts. The > above expressions are much simpler than the ones I REALLY want > Mathematica's help in simplifying. If I use this ComplexExpand > command, then I'm going to have to recombine them into complex numbers > again, which would be very very bad. > > Thanks, > Roy > -- 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**:**Trouble computing conjugates***From:*Roy <sarahroy@earthlink.net>