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Re: Complex diagram

  • To: mathgroup at smc.vnet.net
  • Subject: [mg123471] Re: Complex diagram
  • From: Murray Eisenberg <murray at math.umass.edu>
  • Date: Thu, 8 Dec 2011 05:25:41 -0500 (EST)
  • Delivered-to: l-mathgroup@mail-archive0.wolfram.com
  • References: <201112071115.GAA04253@smc.vnet.net>
  • Reply-to: murray at math.umass.edu

The easiest way is to use David Park's "Presentations" application,
which nicely handles complex variables. See

   http://home.comcast.net/~djmpark/DrawGraphicsPage.html

and the pdf version of his example "Complex Function Plot" at:

   http://www.st-andrews.ac.uk/~pl10/c/djmpark/

For example:

   <<Presentations`

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

    Draw2D[{DrawCartesianMap[f[z], {z, -(1 + I), 1 + I}]},
           Axes -> True]

Typically, you'd want to draw grids, either rectangular (as here) or
polar in the domain and the range, and highlight particular curves or
other sets in the domain and their images in the range. For example:

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

To do the polar grid, you'd just change DrawCartesianMap to DrawPolarMap 
and specify the range of z in terms of polar coordinates.

Otherwise, with bare Mathematica, you have to use ParametricPlot. For
example:

   ParametricPlot[Through[{Re, Im}[2 x + 3 y I]], {x, -1, 1}, {y, -1, 1}]


On 12/7/11 6:15 AM, =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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