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From: Pratip Chakraborty on 30 May 2010 06:47
Dear Dave,

here goes my solution.

func[c_?NumericQ,m_?NumericQ,n_?NumericQ]:=FindRoot[{a-b==2*Pi*(m-n)+ArcTan[(a-b)/c],a+b==2*Pi*(m+n)},{{a,2
I+1},{b,-2 I+1}}]
Needs["PlotLegends`"];
Clear[m,n];
Error={a-b==2*Pi*(m-n)+ArcTan[(a-b)/c],a+b==2*Pi*(m+n)}/.a_==b_-> a-b;
(* Lets vary the c from 5 to 100 with a distance between points being .1 *)
cval=Cases[Range[5,100,.1],Except[0]];
m=3;n=5;
{Error1,Error2}=Map[(Error/.c-> #/.func[#,m,n])&,cval]//Transpose;
{AIm,BIm}=Map[({Im[a],Im[b]}/.func[#,m,n])&,cval]//Transpose;
(* Lets plot the imaginary parts *)
ListLinePlot[{Transpose[{cval,AIm}],Transpose[{cval,BIm}]},Frame->
True,Axes-> None,PlotRange-> All,PlotLegend->{"Im(a)",
"Im(b)"},LegendPosition->{1.1,-0.4}]

If you want the real part also

{ARe,BRe}=Map[({Re[a],Re[b]}/.func[#,m,n])&,cval]//Transpose;
(* Lets plot the real parts *)
ListLinePlot[{Transpose[{cval,ARe}],Transpose[{cval,BRe}]},Frame->
True,Axes-> None,PlotRange-> All,PlotLegend->{"Re(a)",
"Re(b)"},LegendPosition->{1.1,-0.4}]


Regards,

Pratip

On Sat, May 29, 2010 at 10:43 AM, JustanotherDave
<david.holdaway(a)gmail.com>wrote:

> I'm having trouble getting Mathematica to plot what I would like from
> a system of equations. I have the function
>
> f[c_?NumericQ, m_?NumericQ, n_?NumericQ] :=
> FindRoot[{a - b == 2*Pi*(m - n) + ArcTan[(a - b)/c],
> a + b == 2*Pi*(m + n)}, {{a, 2 I + 1}, {b, -2 I + 1}}]
>
> Which evaluates to something like {a -> 13.333 + 2.99972*10^-20 I, b -
> > -13.333 - 2.99972*10^-20 I}
> What I would like is to be able to plot the imaginary values of a and
> b on the same graph (varying the parameter c, keeping m and n
> constant) but I'm not sure how to convert the FindRoot output to
> plotable values
>
>
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