plotting roots of complex nonlinear equation

• To: mathgroup at christensen.cybernetics.net
• Subject: [mg629] plotting roots of complex nonlinear equation
• From: Roque Donizete de Oliveira <oliveria at engin.umich.edu>
• Date: Sat, 1 Apr 1995 17:24:25 -0500

```I have a complex nonlinear equation, f[z,p] = 0, that I want
to solve for complex z=x + I*y, as a function of real parameter p
(p varies from 0.5 to 1.5). This describes the problem (in MMA):

g[z_]    := I Sqrt[Pi] Exp[-z^2] ( 1 + Erf[I z] )
f[z_,p_] := z^2 - 1 - 0.348 * g[3.87*(p-1)/(p*z)] / (z * p^2)

This equation has multiple solutions. I want to plot a few (2 or 3)
branches on the same plot, i.e., I want to plot x versus p in one plot
and y versus p in another plot. Each branch should use a different
color for plotting.

I haven't been able to find a concise way of doing this, with either
Maple or Mathematica. I got lost in the bookkeeping of the solutions.

I know how to solve it, I just can't find a clean way to display
the results.

Any help is appreciated (and you don't even have to use the function
above).

Thanks.

Roque
oliveria at engin.umich.edu

```

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