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MathGroup Archive 2004

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Re: Complex plotting

  • To: mathgroup at smc.vnet.net
  • Subject: [mg52291] Re: Complex plotting
  • From: Peter Pein <petsie at arcor.de>
  • Date: Sun, 21 Nov 2004 07:23:27 -0500 (EST)
  • References: <cnn11e$8qb$1@smc.vnet.net>
  • Sender: owner-wri-mathgroup at wolfram.com

Diana wrote:
> Mathematica folks,
> 
> I am trying to plot the function:
> 
> E^(3 z)/(1 + E^z) where z ranges from z = R (>0) to z = R + 2 Pi I.
> 
> When z = R, the value of the function is E^(3 R)/(1 + E^R)
> 
> When z = R + Pi I, the value of the function is E^(3 R)/(-1 + E^R)
> 
> When z = R + 2 Pi I, the value of the function is E^(3 R)/(1 + E^R) again.
> 
> I am trying to show with a plot that the magnitude of the function achieves
> its maximum at z = R + Pi I.
> 
> I have tried using ComplexMap, but perhaps don't know how to fully utilize
> it.
> 
> Help would be appreciated.
> 
> Diana
> 

g[x_] := (Abs[#1^3/(1 + #1)] & )[E^x];

Block[{$DisplayFunction = Identity},
    p1 = Plot3D[g[R + I*t], {R, -(1/2), 1}, {t, 0, 2*Pi},
       ViewPoint -> {-1.3, 1, 1}, Mesh -> False, PlotPoints -> 64,
       Ticks -> {Automatic, Table[(k*Pi)/2, {k, 0, 4}], Automatic},
       PlotRange -> {0, 12}];
    p2 = ParametricPlot3D[{r, Pi, g[r + I*Pi]}, {r, -(1/2), 1}];
];

Show[p1, p2];

Should give a first impression where your function has its maximum magnitude.

-- 
Peter Pein
10245 Berlin


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