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Re: Simple questions with Complex Numbers

• To: mathgroup at smc.vnet.net
• Subject: [mg50886] Re: [mg50876] Simple questions with Complex Numbers
• From: "David Park" <djmp at earthlink.net>
• Date: Sun, 26 Sep 2004 05:31:47 -0400 (EDT)
• Sender: owner-wri-mathgroup at wolfram.com

Sunil,

When working with complex expressions, you will almost always want to and
need to use ComplexExpand. There is also a Conjugate command. So..

z = s + I t

ComplexExpand[z Conjugate[z]]
s^2 + t^2

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

From: Sunil Pinnamaneni [mailto:pinnama at cims.nyu.edu]
To: mathgroup at smc.vnet.net


I'm having difficulty getting mathematica to do simplifications with Complex
Numbers. For instance,

z = s+ I t;
zbar = s- I t;
FullSimplify[Re[1/(z zbar)]]

yields

Re[1/(s^2 +t^2)]

Is there any way to get Mathematica to yield the result 1/(s^2 +t^2) without
the Re? It seems like Mathematica should have been programmed to do easy
simplifications using Complex Numbers.

I'm interested in finding the Real part of expressions like 1/z^5, but
Mathematica doesn't seem to want to multiply the denominator by the
conjugate, and carry out the simpification.

Can Mathematica do such things, or does one have to specifically program it
to handle these simplifications.

Thanks,
Sunil