Re: Symbolic complex conjugation

• To: mathgroup at smc.vnet.net
• Subject: [mg26153] Re: Symbolic complex conjugation
• From: Jens-Peer Kuska <kuska at informatik.uni-leipzig.de>
• Date: Thu, 30 Nov 2000 01:03:59 -0500 (EST)
• Organization: Universitaet Leipzig
• References: <8vvpo5\$34g@smc.vnet.net>
• Sender: owner-wri-mathgroup at wolfram.com

```Hi,

> Suppose one wishes to do symbolic complex conjugation on a complicated
> symbolic expression in which all symbols are assumed purely real -- that
> is, given a symbolic expression of arbitrary complexity with multiple
> instances of I occuring inside it, change every instance of I to -I, and
> nothing more.
>
> The best approach I'm aware of seems to be the method described in the
> 4.0 Help files, namely
>
>       new_expr = old_expr  /. Complex[0, n_] -> -Complex[0, n]
>
> Is there a better approach than this?

No.

>
> And, for educational purposes, can someone explain how and why this
> approach works?  In particular, why isn't the rule something like
>
>       Complex[a_, b_] -> Complex[a, -b]
>
> Is the "0" significant?  Is the "n" supposed to be integer?

Yes because:

FullForm[a + I*b]

is

Plus[a, Times[Complex[0, 1], b]]

Complex[] is always a number, you cant have Copmplex[a_Symbol,b_Symbol]
and so your symbolic expression include only I or Complex[0,1] and
no other objects with head Complex[].

Regards
Jens

```

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