Re: Simplify[ {Re[Sqrt[-1 + eta^2]], Im[Sqrt[-1 + eta^2]]}, eta<1]

• To: mathgroup at smc.vnet.net
• Subject: [mg50631] Re: Simplify[ {Re[Sqrt[-1 + eta^2]], Im[Sqrt[-1 + eta^2]]}, eta<1]
• From: Jens-Peer Kuska <kuska at informatik.uni-leipzig.de>
• Date: Wed, 15 Sep 2004 01:49:25 -0400 (EDT)
• Organization: Universitaet Leipzig
• References: <ci3ele\$e41\$1@smc.vnet.net>
• Sender: owner-wri-mathgroup at wolfram.com

```Hi,

FullSimplify[test, eta < 1 && eta > -1]

??

Regards
Jens

peteraptaker wrote:
>
> Have I missed something - my apologies if this is answered in a FAQ
> I want to make the simple Re and Im parts simplify properly?
>
> test =
>   {Re[Sqrt[-1 + eta^2]], Im[Sqrt[-1 + eta^2]]}
>
> FullSimplify[test, eta > 1]
> gives*{Sqrt[-1 + eta^2], 0}
>
> But
> FullSimplify[test, eta < 1]
> gives
> {Re[Sqrt[-1 + eta^2]], Im[Sqrt[-1 + eta^2]]}
>
> Needs["Algebra`ReIm`"] does not seem to help
>
> Real numbers demonstrate what should happen:
> test) /. {{eta -> 0.1}, {eta -> 2}}
> {{0., 0.99498743710662}, {Sqrt[3], 0}}

```

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