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/