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Misbehavior of Conjugate[Exp[I x]]

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  • Subject: Misbehavior of Conjugate[Exp[I x]]
  • From: mek at (Mark E. Kotanchek)
  • Date: Tue, 2 Mar 93 16:42:07 -0500

Hi folks,

Right now I'm swearing at mma because taking the conjugate of a  
complex exponential doesn't simplify much, i.e.,

   Conjugate[Exp[I x]]
              I x
   Conjugate[E   ]

Ok, you say this is because "x" could be complex; however, if I load  
Algebra`ReIm` and define

   x /: Im[x] = 0

I still get a result of

   Conjugate[Exp[I x]]
              I x
   Conjugate[E   ]   


Now taking the Re[Exp[I x]] results in Cos[x] so mma at least  
understands that x is now defined to be real. Is there something I  
don't understand here or is this a deficiency in how mma handles (or  
doesn't handle) complex-valued equations.

I'm also trying to do a series expansion of a complex-valued function  
of theta about theta = 0, Arg[rho[theta]]] wherein mma gives me  
answers involving the derivatives of "Arg". There may be subtleties  
here; however, I suspect that a major source of the problem is that  
mma is woefully deficient with respect to understanding domains. (Too  
bad Derive isn't available for the NeXT!)

Any suggestions or comments?

Grumble, mutter, etc.,

Mark Kotanchek
Guidance & Control Dept - 363 ASB
Applied Research Lab/Penn State
P.O. Box 30
State College, PA 16804

e-mail:	mek at (NeXTmail)
TEL:	(814)863-0682
FAX:	(814)863-7843

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