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MathGroup Archive 2005

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Re: Complex Oddity

  • To: mathgroup at smc.vnet.net
  • Subject: [mg57491] Re: Complex Oddity
  • From: Jean-Marc Gulliet <jeanmarc.gulliet at 9online.fr>
  • Date: Sun, 29 May 2005 21:00:08 -0400 (EDT)
  • Organization: New York University
  • References: <d79enu$lbl$1@smc.vnet.net>
  • Reply-to: jmg336 at nyu.edu
  • Sender: owner-wri-mathgroup at wolfram.com

John Reed wrote:
> 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 
> 

Hi John,

the expression z = a + I y may not be translated internally as you expect:

In[1]:= z = x + I y

Out[1]= x+\[ImaginaryI] y

In[2]:= FullForm[z]

Out[2]= Plus[x,Times[Complex[0,1],y]]

You could try

In[3]:= imagPart = z/.{a_+I b_\[Rule]b}

Out[3]= y

In[4]:= realPart=z/.{a_+I b_\[Rule]a}

Out[4]= x

Best regards,
/J.M.


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