Re: Simplifying expression involving Log and I
- To: mathgroup at smc.vnet.net
- Subject: [mg38018] Re: [mg38010] Simplifying expression involving Log and I
- From: Andrzej Kozlowski <andrzej at tuins.ac.jp>
- Date: Tue, 26 Nov 2002 00:48:42 -0500 (EST)
- Sender: owner-wri-mathgroup at wolfram.com
This will take you pretty close:
FullSimplify[ComplexExpand[
d*Pi + I*d*(Log[M] - 2*Log[(-I)*Sqrt[(M*r)/d] +
Sqrt[M - (M*r)/d]]), TargetFunctions -> {Re, Im}],
M > 0 && 0 < r < d]
d*(Pi + 2*ArcTan[Sqrt[M - (M*r)/d], -Sqrt[(M*r)/d]])
Still, there appears to be something missing among the rules
FullSimplify is applying.
It seems related to the following behaviour, that certianly suggests a
bug:
FullSimplify[ArcTan[x, y], {x > 0, y < 0}]
ArcTan[x, y]
FullSimplify[ArcTan[2*x, 2*y], {x > 0, y < 0}]
ArcTan[y/x]
On Monday, November 25, 2002, at 03:58 PM, Dave Snead wrote:
> Hi,
>
> I'm trying to simplify (M, r, d are positive reals with r<d)
> d*Pi + I*d*(Log[M] - 2*Log[(-I)*Sqrt[(M*r)/d] + Sqrt[M - (M*r)/d]])
>
> to
>
> 2*d*ArcCos[Sqrt[r/d]]
>
> I've tried applying
>
> FullSimplify[#,M>0 && 0<r<d]&
>
> and
>
> ExpToTrig
>
> but Mathematica won't get rid of the Log and the I and give me the
> ArcCos.
>
> Does anyone know which Mathematica functions to apply to my expression
> to
> give me the simplification I want?
>
> Thanks in advance.
>
>
>
>
>
>
>
Andrzej Kozlowski
Yokohama, Japan
http://www.mimuw.edu.pl/~akoz/
http://platon.c.u-tokyo.ac.jp/andrzej/