FindRoot on complex 'interval'

*To*: mathgroup at smc.vnet.net*Subject*: [mg36943] FindRoot on complex 'interval'*From*: David J Strozzi <dstrrozzi at MIT.EDU>*Date*: Wed, 2 Oct 2002 03:33:44 -0400 (EDT)*Sender*: owner-wri-mathgroup at wolfram.com

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.

**Follow-Ups**:**Re: FindRoot on complex 'interval'***From:*Daniel Lichtblau <danl@wolfram.com>

**Re: FindRoot on complex 'interval'***From:*Selwyn Hollis <selwynh@earthlink.net>