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Re: Complex diagram

  • To: mathgroup at smc.vnet.net
  • Subject: [mg123476] Re: Complex diagram
  • From: Murray Eisenberg <murray at math.umass.edu>
  • Date: Thu, 8 Dec 2011 05:26:41 -0500 (EST)
  • Delivered-to: l-mathgroup@mail-archive0.wolfram.com
  • References: <201112080022.TAA12699@smc.vnet.net>
  • Reply-to: murray at math.umass.edu

I my original reply (not yet posted by the moderator) to MathGroup, I
make a mistake in the code for using Presentations that was supposed to
show the unit circle and its image. That code showed another circle as
image, which of course is wrong.

Instead of using ComplexCircle, I need to use ComplexCurve:

   <<Presentations`

   f[z_] := 2 Re[z] + 3 Im[z] I

   domain = {DrawCartesianMap[z, {z, -(1 + I), 1 + I}], Red,
             ComplexCurve[Exp[I t], {t, 0, 2 Pi}]};
   image = domain // ComplexMap[f];
   GraphicsRow[{Draw2D[{domain}, Axes -> True],
                Draw2D[{image}, Axes -> True]}]

The reason is that the Presentation function ComplexMap[f] merely
applies the complex function f to the center of the circle
ComplexCircle[0,1] and then forms another circle with that image point
and the same radius as the original one.

For ComplexCurve[...], on the other hand, ComplexMap[f] samples points
on the curve -- here the unit circle -- and calculates the image of each =

of those points.


On 12/7/11 7:22 PM, =E9=81=93 =E5=8E=9A wrote:
> Can we draw complex funtions's diagram in Mathematica?
>
> For example, draw the picture of z=2*x+I*3*y
>

--
Murray Eisenberg                     murray at math.umass.edu
Mathematics & Statistics Dept.
Lederle Graduate Research Tower      phone 413 549-1020 (H)
University of Massachusetts                413 545-2859 (W)
710 North Pleasant Street            fax   413 545-1801
Amherst, MA 01003-9305




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