Misbehavior of Conjugate[Exp[I x]]

• To: mathgroup at yoda.physics.unc.edu
• Subject: Misbehavior of Conjugate[Exp[I x]]
• From: mek at guinan.psu.edu (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.,

In[35]:=
Conjugate[Exp[I x]]
Out[35]=
I x
Conjugate[E   ]

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

In[36]:=
x /: Im[x] = 0
Out[36]=
0

I still get a result of

In[37]:=
Conjugate[Exp[I x]]
Out[37]=
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!)

Grumble, mutter, etc.,

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

e-mail:	mek at guinan.psu.edu (NeXTmail)
TEL:	(814)863-0682
FAX:	(814)863-7843

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