Figure 10.18. The transformation w = f(z) = arcsin(z) is a one-to-one conformal
mapping of the first quadrant x > 0, y > 0 onto the semi-infinite strip |u| < , v > 0.

The image is traced using a graph.

 Thus, the image of the first quadrant x > 0, y > 0 is the semi-infinite strip |u| < , v > 0.

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(c) John Mathews, 1998