Re: Getting simple answers from Reduce, ComplexExpand and FullSimplify

• To: mathgroup at smc.vnet.net
• Subject: [mg57871] Re: Getting simple answers from Reduce, ComplexExpand and FullSimplify
• From: Paul Abbott <paul at physics.uwa.edu.au>
• Date: Sat, 11 Jun 2005 03:35:25 -0400 (EDT)
• Organization: The University of Western Australia
• References: <d893st\$t26\$1@smc.vnet.net>
• Sender: owner-wri-mathgroup at wolfram.com

```In article <d893st\$t26\$1 at smc.vnet.net>,
"Hugh Goyder" <h.g.d.goyder at cranfield.ac.uk> wrote:

> Below the expression ex has roots, rts, where n in an integer and the
> constant a is in the interval 0 < a <1. We may check this using FullSimplify
> as follows.
>
> ex=2 Cos[z]+I a Sin[z];
>
> rts=z ->Pi(2n-1)/2 + I Log[(2+a)/(2-a)]/2;
>
> FullSimplify[0 == ex/.rts,Element[n,Integers]]

The following works for any a:

ex = 2 Cos[z]+I a Sin[z];

rts = z -> Pi(2n-1)/2 + I Log[(2+a)/(2-a)]/2;

Simplify[ex /. rts, Element[n,Integers]];

FullSimplify[% == 0]

so this result holds for arbitrary complex a.

Cheers,
Paul

--
Paul Abbott                                      Phone: +61 8 6488 2734
School of Physics, M013                            Fax: +61 8 6488 1014
The University of Western Australia         (CRICOS Provider No 00126G)
AUSTRALIA                               http://physics.uwa.edu.au/~paul
http://InternationalMathematicaSymposium.org/IMS2005/

```

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