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Topic: complex conjugation by star
Replies: 7   Last Post: Apr 23, 2014 4:52 AM

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Murray Eisenberg

Posts: 2,105
Registered: 12/6/04
Re: complex conjugation by star
Posted: Apr 20, 2014 4:47 AM
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Mathematica already has a built-in Conjugate function used in the form Conjugate[z] as well as a suffix operator with a star that may be typed Esc co Esc or \[Conjugate].

You should not use ordinary lower-case i to denote the imaginary unit; type either I or Esc ii Esc. And it's best to avoid using upper-case letters A, B, G, etc., to avoid clashes with built-in Mathematica symbols.

Automatically, Mathematica will do some of what you want:

{a, b, g}\[Conjugate]
(* {Conjugate[a], Conjugate[b], Conjugate[g]} *)

Evaluating an expression such as Element[a, Complexes] by itself accomplishes nothing and is _not_ "remembered" in any way for further calculations. The way to indicate symbols are to be treated as reals when doing complex-algebra calculations is to use ComplexExpand. Thus:

(x + I y)\[Conjugate] // ComplexExpand
(* x - I y *)

With the built-in Conjugate function, for your example with BesselJ, you'd need to use:

On Apr 18, 2014, at 1:46 AM, Brambilla Roberto Luigi (RSE) <> wrote:

> I have defined the following useful star complex-conjugation (common star exponent notation)
> f_*:=f/.Complex[u_,v_]->Complex[u,-v]
> and it works fine. For example BesselJ[2,x+I y]* gives BesselJ[2,x-I y] etc...(x,y defined/undefined).
> Also it is listable on number lists
> {1+i2, 5+i6}* gives {1-i2, 5-i6} .
> Unfortunately it does not work on symbols, i.e.
> A* gives A even if I have defined A as a complex number by means of Element[A, Complexes].
> Similarly if I define Element[{A,B,G}, Complexes]
> {A,B,G}* gives {A,B,G} and (A+B+G)* gives A+B+G.
> I'd like to obtain {A*,B*,G*} and A*+B*+G* ( ! )
> Is it possible to fix this deficiency, unpleasant in manipulating general expressions where is not known
> if symbols represent real or complex variables ?
> Many thanks!
> Rob
> RSE SpA ha adottato il Modello Organizzativo ai sensi del =

D.Lgs.231/2001, inforza del quale l'assunzione di obbligazioni da parte =
della Societ=E0 avviene con firma di un procuratore, munito di idonei =

Murray Eisenberg
Mathematics & Statistics Dept.
Lederle Graduate Research Tower phone 240 246-7240 (H)
University of Massachusetts
710 North Pleasant Street
Amherst, MA 01003-9305

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