Re: Symbolic complex conjugation?

• To: mathgroup at smc.vnet.net
• Subject: [mg89974] Re: Symbolic complex conjugation?
• From: magma <maderri2 at gmail.com>
• Date: Wed, 25 Jun 2008 06:30:01 -0400 (EDT)
• References: <g3q7vb\$aus\$1@smc.vnet.net>

```On Jun 24, 9:32 am, AES <sieg... at stanford.edu> wrote:
> I'm sorry, but I just don't understand why the following test case works
> just fine:
>
> [In copying it, I've substituted "Isymbol" for the \[ImaginaryI] that
> actually appears in the Out[] cells.]
>
>    In[202]:= eqna={a+I b==0};
>    solna=Solve[eqna,b];
>    b=b/.solna[[1]];
>    bStar=b/.{I->-I};
>    {b, Star}
>
>    Out[205]={ -Isymbol a, Isymbol a }
>
> but the actual calculation that prompted the test case doesn't:
>
>    In[206]:= eqnp={((dwa/2)+I(w-wa))p-I (kappa/(2 w))dN e==0};
>    solnp=Solve[eqnp,p];
>    p=p/.solnp[[1]];
>    pStar=p/.{I->-I}
>
>    Out[208]= { (dN e kappa)/(w (-Isymbol dwa+2 w-2 wa)),
>                         (dN e kappa)/(w (-Isymbol dwa+2 w-2 wa)) }
>
> And actually, I guess my real concern is not understanding "how it
> happens" -- but more "how it can happen" that Mathematica can do
> something this potentially damaging to some innocent user.

Changing I into -I is not a good idea. Never.
In your p you have -I which is internally Complex[0,-1] as you can see
with

p//FullForm

So your I->-I is never carried out.

In your test case b was I a , so the replacement was carried out.

If you want to Conjugate a complex number p, use Conjugate[p] and then
ComplexExpand, if all your variables are supposed to be Real.

ComplexExpand[Conjugate[p]]

will give you the correct answer.

```

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