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Re: equation question


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



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