Re: Trouble computing conjugates

• To: mathgroup at smc.vnet.net
• Subject: [mg88547] Re: Trouble computing conjugates
• From: dh <dh at metrohm.ch>
• Date: Thu, 8 May 2008 04:12:56 -0400 (EDT)
• References: <fvs2k5\$enp\$1@smc.vnet.net>

```
Hi Roy,

mathematica thinks the distributed form is more complicated, therefore,

you get the undistributed form. You may tell mma to distribute by e.g.:

Refine[Conjugate[c1 u1+c2 u2]//Distribute]

hope this helps, Daniel

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

>

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