Re: Trouble computing conjugates

*To*: mathgroup at smc.vnet.net*Subject*: [mg88561] Re: Trouble computing conjugates*From*: "David Park" <djmpark at comcast.net>*Date*: Thu, 8 May 2008 04:15:31 -0400 (EDT)*References*: <fvs2k5$enp$1@smc.vnet.net>

I don't think you need to use $Assumptions or Refine. Just use ComplexExpand. u1 = f + I g; u2 = f - I g; Conjugate[c1 u1] ComplexExpand[%] Conjugate[c1] (Conjugate[f] - I Conjugate[g]) c1 f - I c1 g Conjugate[c1 u1 + u2] ComplexExpand[%] Conjugate[f + c1 (f + I g)] + I Conjugate[g] f + c1 f + I (g - c1 g) -- David Park djmpark at comcast.net http://home.comcast.net/~djmpark/ "Roy" <sarahroy at earthlink.net> wrote in message news:fvs2k5$enp$1 at smc.vnet.net... > 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 >