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

• To: mathgroup at smc.vnet.net
• Subject: [mg48219] Re: proof of formula for log(-t) found in Mathematica?
• From: Erich Neuwirth <erich.neuwirth at univie.ac.at>
• Date: Tue, 18 May 2004 04:16:46 -0400 (EDT)
• References: <c89q4h\$t5b\$1@smc.vnet.net>
• Sender: owner-wri-mathgroup at wolfram.com

Well, if |t|=1,
then the formula is
Log[-t]=I*Arg[-t]
which is the same as
-t=Exp[I*Arg[-t]]
which is the definition of Arg
Log[t^2]/2=Log[|t|],
which you have to add if |t|!=1,
so the formula is correct since
Log[-t]=Log[|-t|*Exp[i*Arg[-t]]=Log[[-t|]+Log[Exp[I*Arg[-t]]=
Log[|t|]+I*Atg[-t]=Log[t^2]/2+I*Atg[-t]

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
>

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