Re: Poles and Complex Factoring
- To: mathgroup at smc.vnet.net
- Subject: [mg52176] Re: [mg6011] Poles and Complex Factoring
- From: godfreyau2003 at hotmail.com (Godfrey)
- Date: Sun, 14 Nov 2004 04:30:12 -0500 (EST)
- References: <5dp3kk$6nq@smc.vnet.net>
- Sender: owner-wri-mathgroup at wolfram.com
On 11 Feb 1997 01:29:40 -0500, peter wrote:
>Dear All,
>
>I know how to calculate the residue of a fuction using Mathematica, but how
can I
>use Mathematica to calculate the order of a complex pole?
>
>It would also be nice for Mathematica to tell me if a particular singularity
is an
>essential singularity, removable singularity or a pole...but this is
not
>necessary; just icing on the cake.
>
>Also, is there a way to factor polynomials with imaginary roots?
>Something like:
>
> Factor[ x^2 + 2x + 10 ] = (x - 1 + 4.5 I)(x - 1 - 4.5 I)
>
>Much thanks in advance!
>
>Peter
>
>--
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determined
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longest.....
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Let x^2 + 2x + 10 = (x-a)(x-b)
Obviously, a and b are the roots of the equation x^2 + 2x + 10 = 0
------ (*)
By quadratic forumula, we can find that the roots of (*)=2+sqrt(10) or
2-sqrt(10)
Therefore,
x^2 + 2x + 10 = {x-[2+sqrt(10)]}{x-[2-sqrt(10)]}
ie. x^2 + 2x + 10 = [x-2-sqrt(10)][x-2+sqrt(10)]
Factorization of other polynomials with imaginary roots can be done in
the same way.