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Trouble computing conjugates

  • To: mathgroup at smc.vnet.net
  • Subject: [mg88515] Trouble computing conjugates
  • From: Roy <sarahroy at earthlink.net>
  • Date: Wed, 7 May 2008 07:07:41 -0400 (EDT)

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


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