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circle = ComplexCircle[0.1, 1/2];
domain = Draw2D[{Opacity[0.6], circle},
   Frame -> True,
   Axes -> True,
   PlotRange -> 2,
   FrameLabel -> {Re, Im},
   PlotLabel -> z, ImageSize -> 200];
image = Draw2D[{Opacity[0.6], circle // ComplexMap[Log]},
   Frame -> True,
   Axes -> True,
   PlotRange -> 4,
   FrameLabel -> {Re, Im},
   PlotLabel -> w,
   ImageSize -> 200];
Row[{domain, image}]

The above code works, creating the following image.

Mathematica graphics

However, if I change the center to the origin:

circle = ComplexCircle[0, 1/2];
domain = Draw2D[{Opacity[0.6], circle},
   Frame -> True,
   Axes -> True,
   PlotRange -> 2,
   FrameLabel -> {Re, Im},
   PlotLabel -> z, ImageSize -> 200];
image = Draw2D[{Opacity[0.6], circle // ComplexMap[Log]},
   Frame -> True,
   Axes -> True,
   PlotRange -> 4,
   FrameLabel -> {Re, Im},
   PlotLabel -> w,
   ImageSize -> 200];
Row[{domain, image}]

The code fails, giving the following error message:

Coordinate {DirectedInfinity[-1], 0} should be a pair of numbers, or a Scaled or Offset form.

But this works with center at the origin:

circle = {Red, Thickness[0.02], 
   ComplexCurve[Exp[I t], {t, 0, 2 Pi}]};
domain = Draw2D[{Opacity[0.6], circle},
   Frame -> True,
   Axes -> True,
   PlotRange -> 2,
   FrameLabel -> {Re, Im},
   PlotLabel -> z, ImageSize -> 200];
image = Draw2D[{Opacity[0.6], circle // ComplexMap[Log]},
   Frame -> True,
   Axes -> True,
   PlotRange -> 4,
   FrameLabel -> {Re, Im},
   PlotLabel -> w,
   ImageSize -> 200];
Row[{domain, image}]

Producing this image:

Mathematica graphics

What's going on?

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migrated from meta.mathematica.stackexchange.com Jan 20 '13 at 0:09

This question came from our discussion, support, and feature requests site for users of Mathematica.

    
I think it is this. In the circle case, the ComplexMap[Log] takes Log of the center, Log of the radius, and just draws another circle with the results. Hence, Log[0] is the problem? –  David Jan 20 '13 at 2:17
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