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Symbolic complex conjugation

  • To: mathgroup at
  • Subject: [mg26125] Symbolic complex conjugation
  • From: "A. E. Siegman" <siegman at>
  • Date: Tue, 28 Nov 2000 01:56:10 -0500 (EST)
  • Organization: Stanford University
  • Sender: owner-wri-mathgroup at

Suppose one wishes to do symbolic complex conjugation on a complicated 
symbolic expression in which all symbols are assumed purely real -- that 
is, given a symbolic expression of arbitrary complexity with multiple 
instances of I occuring inside it, change every instance of I to -I, and 
nothing more.

The best approach I'm aware of seems to be the method described in the 
4.0 Help files, namely

      new_expr = old_expr  /. Complex[0, n_] -> -Complex[0, n]

Is there a better approach than this?

And, for educational purposes, can someone explain how and why this 
approach works?  In particular, why isn't the rule something like

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

Is the "0" significant?  Is the "n" supposed to be integer?

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