Re: equation question

*To*: mathgroup at smc.vnet.net*Subject*: [mg69973] Re: [mg69921] equation question*From*: Daniel Lichtblau <danl at wolfram.com>*Date*: Thu, 28 Sep 2006 06:16:47 -0400 (EDT)*References*: <200609271005.GAA00230@smc.vnet.net>

dimmechan at yahoo.com wrote: > Hello. > > Consider the following simple examples of FindRoot application. > > FindRoot[Sin[x] == 2, {x, I}] > {x -> 1.5707963267948966 + 1.3169578969248168*I} > > FindRoot[Sin[x^2] == 2, {x, I + 1}] > {x -> 1.3454777060580754 + 0.4894016047219337*I} > > FindRoot[Sin[x^2] == 2, {x, 3*I + 2}] > {x -> 0.3004695589886017 + 2.1914997002654357*I} > > Is it possible for FindRoot (or in general in another way) to search > for solutions > in the complex plane in an particular domain e.g. searching in the > domain that > is made by the lines Re[x]=a1, Re[x]=a2 and Im[x]=b1, Im[b]=b2 ? > > I really appreciate any assistance. > > Regards > Dimitris You can set it up as a minimization of a square (for multiple equations, a sum of squares) and use NMinimize, which handles such constraints. Example: In[1]:= NMinimize[{Abs[(Sin[(a+I*b)^2]-2)^2], {5<=a<=9, 0<=b<=2}}, {a,b}] -17 Out[1]= {3.89097 10 , {a -> 5.16912, b -> 0.127387}} Daniel Lichtblau Wolfram Research

**Follow-Ups**:**Re: Re: equation question***From:*Andrzej Kozlowski <akoz@mimuw.edu.pl>

**Re: Re: equation question***From:*Andrzej Kozlowski <akoz@mimuw.edu.pl>

**References**:**equation question***From:*dimmechan@yahoo.com