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

• To: mathgroup at smc.vnet.net
• Subject: [mg50632] Re: [mg50617] Simplify[ {Re[Sqrt[-1 + eta^2]], Im[Sqrt[-1 + eta^2]]}, eta<1]
• From: Bob Hanlon <hanlonr at cox.net>
• Date: Wed, 15 Sep 2004 01:49:27 -0400 (EDT)
• Reply-to: hanlonr at cox.net
• Sender: owner-wri-mathgroup at wolfram.com

```test={Re[Sqrt[-1+eta^2]],
Im[Sqrt[-1+eta^2]]};

Simplify[test,
-1 < eta < 1]

{0, Sqrt[1 - eta^2]}

Simplify[test,
eta <= -1 || 1 <= eta]

{Sqrt[eta^2 - 1], 0}

Simplify[test,
Element[eta, Reals] && Abs[eta] < 1]

{0, Sqrt[1 - eta^2]}

Simplify[test,
Element[eta, Reals] && Abs[eta] >= 1]

{Sqrt[eta^2 - 1], 0}

Bob Hanlon

>
> From: psa at laplacian.co.uk (peteraptaker)
To: mathgroup at smc.vnet.net
> Date: 2004/09/13 Mon AM 02:19:33 EDT
> To: mathgroup at smc.vnet.net
> Subject: [mg50632] [mg50617] Simplify[ {Re[Sqrt[-1 + eta^2]], Im[Sqrt[-1 + eta^2]]}, eta<1]
>
> 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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