Re: Simplifying expression involving Log and I
- To: mathgroup at smc.vnet.net
- Subject: [mg38029] Re: [mg38010] Simplifying expression involving Log and I
- From: Sseziwa Mukasa <mukasa at jeol.com>
- Date: Tue, 26 Nov 2002 00:49:31 -0500 (EST)
- Sender: owner-wri-mathgroup at wolfram.com
On Monday, November 25, 2002, at 01:58 AM, 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.
>
I can't get the form you want but
FullSimplify[ComplexExpand[d*Pi + I*d*(Log[M] -
2*Log[(-I)*Sqrt[(M*r)/d] + Sqrt[M - (M*r)/d]])],{M>0&&r>0&&d>0&&r<d}]
will get you to
d*(Pi+2 Arg[-I*Sqrt[M*r/d]+Sqrt[M-M*r/d]])
Regards,
Ssezi