RE: complex coefficients and rules...

• To: mathgroup at smc.vnet.net
• Subject: [mg28222] RE: [mg28203] complex coefficients and rules...
• From: "David Park" <djmp at earthlink.net>
• Date: Thu, 5 Apr 2001 03:00:35 -0400 (EDT)
• Sender: owner-wri-mathgroup at wolfram.com

```Richard,

This is one possible method:

myConjugate[expr_] := TrigToExp[ComplexExpand[Conjugate[expr]]]

Exp[-I y] + Exp[-4 I z] // myConjugate
E^(I*y) + E^(4*I*z)

ComplexExpand will expand assuming that variables are real. (You can specify
which ones are complex.) TrigToExp puts the result back into exponential
form, if that is what you want.

A second approach is simple to make your "cumbersome" procedure into a less
cumbersome routine.

myConjugate2[expr_] := expr /. Complex[a_, b_] ->
Complex[a, -b]

Exp[-I y] + Exp[-4 I z] // myConjugate2
E^(I*y) + E^(4*I*z)

David Park

> From: Richard Easther [mailto:easther at physics.columbia.edu]
To: mathgroup at smc.vnet.net
>
> Hi,
>
> I am having some trouble applying some simple rules to complex
> expressions.
>
> For instance,
>
>  Exp[-4 I y] /. I-> -I
>
> yields
>
>  Exp[-4 I y]
>
> This seemed a bit odd, so I looked at the "full form" and found,
>
> Power[E, Times[Complex[0, -4], y]]
>
> However, trying the match
>
>  Exp[-4 I y] /. a_ I -> -a I
>
> doesn't work either, since FullForm[a I ]  is Times[Complex[0, -1], a]
> and so the patterns do not match.
>
> All I want is a simple complex conjugate (the Conjugate function does
> not assume that y is real), that maps I->-I. The more tricky
>
>  Exp[-4 I y] /. Complex[a_ ,b_] -> Complex[a,-b]
>
> does work, but it is seems a little cumbersome.
>
> In any case my question is: is there a general way to avoid having to do
> this, or is Mathematica always going to assume that any algebraic
> constant is potentially complex?
>
> Richard
>

```

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