       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:= NMinimize[{Abs[(Sin[(a+I*b)^2]-2)^2],
{5<=a<=9, 0<=b<=2}}, {a,b}]
-17
Out= {3.89097 10   , {a -> 5.16912, b -> 0.127387}}

Daniel Lichtblau
Wolfram Research

```

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