       Re: Complex Oddity

• To: mathgroup at smc.vnet.net
• Subject: [mg57471] Re: [mg57455] Complex Oddity
• From: Bob Hanlon <hanlonr at cox.net>
• Date: Sun, 29 May 2005 01:03:29 -0400 (EDT)
• Reply-to: hanlonr at cox.net
• Sender: owner-wri-mathgroup at wolfram.com

Whenever a replacement does not seem to work, look at the FullForm and you
will usually see why it works the way that it does.

(a+b*I)//FullForm

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

To define a variable as real, use TagSet to define upvalues

x /: Re[x]=x;
x /: Im[x]=0;
y /: Re[y]=y;
y /: Im[y]=0;

z=x+y*I;

{Re[z],Im[z]}

{x,y}

or use Simplify with assumptions

z=a+b*I;

Simplify[{Re[z],Im[z]}, Element[{a,b}, Reals]]

{a,b}

Bob Hanlon

>
> From: "John Reed" <nospamjreed at alum.mit.edu>
To: mathgroup at smc.vnet.net
> Date: 2005/05/28 Sat AM 05:39:32 EDT
> Subject: [mg57471] [mg57455] Complex Oddity
>
> I was trying to separate the real and imaginary parts of a complicated
> expression, and ended up with something strange.  Here is a short version
of
> what happened.
>
> Let z = x + I y, then realPart = z /. {Complex[a_,b_]->a} gives realPart =
> x.  Great!
>
> Now, try imagPart = z /. {Complex[a_,b_]->b}  returns with imagPart = x +
y.
> Oops
>
> In my original expression, it was harder to see, but the same error was
> occuring.  What I tried first was using Re[z] and Im[z], but then I have to
> work with Im[y] and Im[x].  It seems to me two things need to be done
here.
> First, be able to assign variables so that they always stay real or else
> indicate an error is occuring if they turn out to be complex, and second do
> something to avoid errors like the above.  I have to say that I don't trust
> Mathematica's answers as much as I did before this came up. Now I feel like
> I better have a good idea of what the answer is before I  trust Mathematica.
>
> John Reed
>
>

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