Example 10.8. The transformation is a one-to-one
conformal mapping of the horizontal strip onto the disk .
Furthermore, the x-axis is mapped onto the lower semicircle bounding the disk,
and the line is mapped onto the upper semicircle.

To show w = f(z) = is one-to-one conformal we need to find the inverse function.

The image is traced using a graph.

 Thus, the image of the horizontal strip is the disk |w| < 1.

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(c) John Mathews, 1998, 2006