- #1

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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.

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- Thread starter Storm Butler
- Start date

- #1

- 78

- 0

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.

- #2

- 1,800

- 53

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}}]
```

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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