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Re: proof of formula for log(-t) found in Mathematica?

• To: mathgroup at smc.vnet.net
• Subject: [mg48203] Re: proof of formula for log(-t) found in Mathematica?
• From: Jens-Peer Kuska <kuska at informatik.uni-leipzig.de>
• Date: Tue, 18 May 2004 04:16:03 -0400 (EDT)
• Organization: Universitaet Leipzig
• References: <c89q4h$t5b$1@smc.vnet.net>
• Reply-to: kuska at informatik.uni-leipzig.de
• Sender: owner-wri-mathgroup at wolfram.com

Hi,

consult a book on complex analysis ...

Log[-t] -> 
Log[ Abs[t]*E^(I*Arg[-t])] -> 
Log[Abs[t]]+I*Arg[-t] -> 
Log[Sqrt[t^2]]+I*Arg[-t] -> 
Log[t^2]/2+I*Arg[-t]

Regards
  Jens

"Roger L. Bagula" wrote:
> 
> I found this while doing work on complex exponents:
> 
> f(t)=Log[-t]=Log[t^2]/2+I*Arg[-t]
> 
> It is a result built into Mathematica.
> I would like to see how it is derived as it seem counter intuitive in
> it's results.
> Respectfully,
> Roger L. Bagula