Re: a question about complex variable

• To: mathgroup at smc.vnet.net
• Subject: [mg21651] Re: a question about complex variable
• From: Harald Giese <giese at dkrz.de>
• Date: Fri, 21 Jan 2000 04:00:00 -0500 (EST)
• Organization: Institut fuer Meereskunde, Universitaet Hamburg
• References: <200001170343.WAA13446@smc.vnet.net> <8615hh\$jtk@smc.vnet.net>
• Sender: owner-wri-mathgroup at wolfram.com

```ZHU Xiaopeng wrote:
>
> In my algebra computation, I obtain a expression:
> C = (- I Cos[2 P] - Sin[2 P]) Tan[A]
> P,A are real variables. Apperently, the argument of C is -2(P+Pi/4) and the
> absolute value of C is Tan[A]. But when I use Arg[C] and Abs[C], Mathematica
> tells me:
>
> Out[41]=Abs[(-I Cos[2 P] - Sin[2 P]) Tan[A]]
> Out[42]=Arg[(-I Cos[2 P] - Sin[2 P]) Tan[A]]
>
> This problem appeared at beginning of the computation. I have no idea to deal
> with it, so the expressions become longer and longer during the computation.
> Can somebody help me?

Hi,

You have to tell Mathematica the property within the expression:

Simplify[Abs[C], {P, A} \[Element] Reals]
or
Simplify[Arg[C], {P, A} \[Element] Reals].

But in your case to no avail, even for "A" being real:
In[]:= Simplify[Tan[(2 n - 1) Pi/2], n \[Element] Integers && n > 1]
Out[]= ComplexInfinity

because they may conflict with predefined Mathematica variables; e.g. C:
"C[i] is the default form for the i-th constant of integration produced
in solving a differential equation with DSolve. "

Regards,
Harald

--- This message was entirely written using recycled electrons ---

Harald Giese
Email: giese at dkrz.de
Phone: +49 (0)40 42838 5796; Fax: +49 (0)40 5605724
Institut fuer Meereskunde der Universitaet Hamburg
(Institute of Oceanography of the University of Hamburg)
Troplowitzstrasse 7, D-22529 Hamburg

```

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