Re: Simplify a complex expression

• To: mathgroup at smc.vnet.net
• Subject: [mg130442] Re: Simplify a complex expression
• From: Peter Pein <petsie at dordos.net>
• Date: Thu, 11 Apr 2013 04:13:08 -0400 (EDT)
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```Am 11.04.2013 00:39, schrieb Polal2is:
> Dear all,
> I have a cumbersome complex expression to simplify the problem is that Conjugate[z] and z are always split I would like a simplified expression involving Abs[z]^2
> as much as possible. How can I tell Mathematica to do it ?
> --
> Thanks a lot in advance
>

Hi,

tell ComplexExpand that z is a complex number and select Abs and Log
as target functions:

In[1]:= ComplexExpand[z + Conjugate[z], z,
TargetFunctions -> {Abs, Log}]

Out[1]= z + Abs[z]^2/z

if this leads to too many Logs, try

In[2]:= z + Conjugate[z] + ArcTan[I z] /. Conjugate :> (Abs[#]^2/# &)

Out[2]= z + Abs[z]^2/z + I ArcTanh[z]