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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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