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Re: Complexes, Reals, FullSimplify

• To: mathgroup at smc.vnet.net
• Subject: [mg48803] Re: [mg48782] Complexes, Reals, FullSimplify
• From: Andrzej Kozlowski <akoz at mimuw.edu.pl>
• Date: Thu, 17 Jun 2004 04:07:15 -0400 (EDT)
• References: <200406160854.EAA12221@smc.vnet.net>
• Sender: owner-wri-mathgroup at wolfram.com

On 16 Jun 2004, at 17:54, Stergios J. Papadakis wrote:

> Dear group,
> I am trying to use expressions of the below form as boundary conditions
> in NDSolve.  I keep getting "non-numerical" errors.  I have tried a lot
> of things and reduced the problem to this:
>
> These give different outputs:
>
> FullSimplify[Re[(1 - 6* I)* Cos[x] - (1 + 2*I)*Sin[(1/2)* 
> x]],Element[x,
> Reals]]
>
> FullSimplify[Re[(1 - 6* I)* Cos[x] - (1 + 2*I)*Sin[0.5*x]],Element[x,
> Reals]]
>
> I get:
>
> \!\(Cos[x] - Sin[x\/2]\)
>
> Re[(1 - 6 \[ImaginaryI]) Cos[x] - (1 + 2 \[ImaginaryI]) Sin[0.5 x]]
>
>
> I think I can get my NDSolve to work if I can make the second
> FullSimplify above give me an output without an Re in it.  Mathematica
> assumes that 0.5 may have some tiny imaginary part and therefore keeps
> everything for full generality.  How do I eliminate
> this?  Note that I have simplified things a lot here, the actual
> expression that I will be using has many terms that all have the
> form above, with many significant digits, which depend on earlier
> calculations.  I have tried using Chop,
>
> FullSimplify[Chop[Re[(1 -
>    6* I)* Cos[x] - (1 + 2*I)*Sin[0.5* x]]], Element[x, Reals]]
>
> And that does not work, I get the same result.
>
>
>
>
>
>
> Thanks,
> Stergios
>
>

The simplest way is to use ComplexExpand; you do not even need 
FullSimplify:

ComplexExpand[Re[(1 - 6* I)* Cos[x] - (1 + 2*I)*Sin[0.5*x]], Element[x,
Reals]]

Cos[x] - Sin[0.5*x]


Andrzej Kozlowski
Chiba, Japan
http://www.mimuw.edu.pl/~akoz/

• References:
  • Complexes, Reals, FullSimplify
    • From: "Stergios J. Papadakis" <stergios.papadakis@jhuapl.edu>