Re: FindRoot on complex 'interval'

• To: mathgroup at smc.vnet.net
• Subject: [mg36948] Re: FindRoot on complex 'interval'
• From: Jens-Peer Kuska <kuska at informatik.uni-leipzig.de>
• Date: Thu, 3 Oct 2002 00:16:24 -0400 (EDT)
• Organization: Universitaet Leipzig
• References: <ane9j1\$kgr\$1@smc.vnet.net>
• Reply-to: kuska at informatik.uni-leipzig.de
• Sender: owner-wri-mathgroup at wolfram.com

```Hi,

and solving the real and imaginary part for for z->x+I*y
with

FindRoot[Evaluate[({Re[#] == 0, Im[#] == 0} &[ z^3 - 1]) /.
z -> x + I y], {x, -3/2, 0}, {y, 0.5, 0.9}]

helps not ?

Regards
Jens

David J Strozzi wrote:
>
> Hello,
>
> I am trying to use FindRoot in mathematica 4.0 to find the zeros of a
> complex-valued function of one complex variable.  In particular, I am
> looking for the one root with a positive imaginary part.  I have a rough
> approximation for where the root should be, and this is good enough to
> give a reasonable guess.
>
> However, there are always two other roots near the one I want - one with
> 0 imaginary part and another with negative imag part.  (For those who
> are interested, the zeros are the roots of the dispersion relation for a
> plasma interacting with a laser).  Sometimes FindRoot picks up one of
> these instead of the one I want.
>
> So, I'd like to tell mathematica to look for a root only in a certain
> rectangular region of the complex plane.  Well, if I could tell it,
> 'look for roots with imag. part > something', I'd be happy too.
>
> I tried specifying complex values for the start and stop points of an
> interval, hoping mathematica would interpret these as the corners of a
> rectangle.  No such luck.
>
> Any help would be greatly appreciated.
>
> I'd also like to point out that this and other issues about complex
> roots are not clearly addressed in the built-in help files.
>
> Thanks much.

```

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