Plotting Complex functions in Mathematica

  • #1
In a few of my books on Complex variables they show how you can look at a complex function as essentially a mapping from what plane to another.

Does anyone know if there would be a way to have mathematica plot how a complex function would transform one plane into the other?

Thanks for any help.
 

Answers and Replies

  • #2
1,800
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In a few of my books on Complex variables they show how you can look at a complex function as essentially a mapping from what plane to another.

Does anyone know if there would be a way to have mathematica plot how a complex function would transform one plane into the other?

Thanks for any help.

You can plot a parametric region. For example, the mapping [itex]e^z\to w[/itex] maps the square region in the z-plane to the washer region in the w-plane:

Code:
w[z_] := Exp[z]; 
p1 = ParametricPlot[{x, y}, {x, 1/10, 1}, {y, -Pi, Pi}, AspectRatio -> 1]; 
p2 = ParametricPlot[{Re[w[z]], Im[w[z]]} /. z -> x + I*y, {x, 1/10, 1}, {y, -Pi, Pi}, 
    PlotRange -> All]; 
myarrow = Show[Graphics[{{Arrow[{{-0.5, 0}, {0.5, 0}}]}, 
      Text[Style["w[z]=\!\(\*SuperscriptBox[\(E\), \(z\)]\)", 20], {0, 0.1}]}]]; 
GraphicsGrid[{{p1, myarrow, p2}}]

attachment.php?attachmentid=63414&d=1383077503.jpg


Ok, now modify my code to map the annulus [itex]1\leq r\leq 5[/itex] in the z-plane under the transformation [itex]1/z\to w[/itex] into the w-plane.
 

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