Re: Mathematica equivalent complexplot

• To: mathgroup at smc.vnet.net
• Subject: [mg57845] Re: Mathematica equivalent complexplot
• From: "David Park" <djmp at earthlink.net>
• Date: Fri, 10 Jun 2005 02:29:09 -0400 (EDT)
• Sender: owner-wri-mathgroup at wolfram.com

```Ron,

I think you are attempting to plot a curve in the complex plane. You can do
it as follows.

Needs["Graphics`Colors`"]

f[x_] = Sin[x + I]
I*Sinh[1 - I*x]

(Mathematica automatically transformed the Sin expression.)

ParametricPlot[{Re[f[x]], Im[f[x]]}, {x, -Pi, Pi},
AspectRatio -> Automatic,
PlotLabel -> SequenceForm["Curve ", f[x], " in Complex Plane"],
Frame -> True,
FrameLabel -> {"Re", "Im"},
FrameTicks -> Automatic,
Background -> Linen,
ImageSize -> 400];

For those who have the complex graphics package, Cardano3, from my web site
below, there is a ComplexCurve routine (suggested by Murray Eisenberg).
Cardano3 also requires DrawGraphics. Then the plot is done with...

Needs["Cardano3`ComplexGraphics`"]

ComplexGraphics[
{ComplexCurve[f[x], {x, -Pi, Pi}]},
PlotLabel -> SequenceForm["Curve ", f[x], " in Complex Plane"],
FrameLabel -> {"Re", "Im"},
FrameTicks -> Automatic,
Background -> Linen];

David Park

From: raf . [mailto:arawak1 at yahoo.com]
To: mathgroup at smc.vnet.net

This is a newbie question, I suppose. I've read as much as I can but cannot
find a straight forward way to implement the complexplot in
Mathematica 5.

An example call could be complexplot(sin(x+i),x=-Pi..Pi) where sin(x+i)
is a typical function f(x) that maps real to complex and -Pi..Pi is the
domain of f, a..b.  Of course, there are various plot options which can
follow and would be included before the closing paren but I think I can
handle that.

So any help would be appreciated.

Thanks much for the response.

Ron Francis

```

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