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RE: Replacement rules with I (sqrt(-1)

  • To: mathgroup at smc.vnet.net
  • Subject: [mg45059] RE: [mg45053] Replacement rules with I (sqrt(-1)
  • From: "David Park" <djmp at earthlink.net>
  • Date: Mon, 15 Dec 2003 06:02:53 -0500 (EST)
  • Sender: owner-wri-mathgroup at wolfram.com

Jean-Michel,

This certainly used to confuse me - until I looked at the FullForm.

I // FullForm
Complex[0, 1]

x + I y // FullForm
Plus[x, Times[Complex[0, 1], y]]

So x + I y contains I and the rule matches.

3 + I // FullForm
Complex[3, 1]

which doesn't contain I (i.e., Complex[0,1]) and therefore the rule doesn't
match. There is a difference between complex expressions and complex
numbers.

You could use the rule:

conjrule = Complex[a_, b_] -> Complex[a, -b]

x + I y /. conjrule
x - I y

3 + I /. conjrule
3 - I

or you also could use:

3 + I // Conjugate
3 - I

x + I y // Conjugate // ComplexExpand
x - I y


David Park
djmp at earthlink.net
http://home.earthlink.net/~djmp/







From: Jean-Michel Collard [mailto:jm at france-paris.org]
To: mathgroup at smc.vnet.net


Can someone explain me this particular behavior :

x+I*y /. I -> -I

x-I y  (*  ok  *)


3+I /. I-> -I

3+I     (*  ????? false  *)

Regards,

J.-M.





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