# Calculus: transformation of complex numbers

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1.) Consider the transformation w = (i - z) / (i + z) . Show that the upper half plane Im z > 0 maps to the disk |w| < 1 and the boundary of the half plane maps to the boundary of the disk (the circle |w| = 1.

2.) Find the image of the semi-infinite strip x > 0, 0 < y < 1, under the transformation w = i/z. Sketch the strip and its image.

Thanks very much

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#### Solution Preview

1.Consider the transformation w = (i - z) / (i + z) . Show that the upper half plane Im z > 0 maps to the disk |w| < 1 and the boundary of the half plane maps to the boundary of the disk (the circle |w| = 1.

Let z = a+bi, where a= Re z and b= Im z. Since Im z > 0, then ...

#### Solution Summary

This solution features transformations for complex numbers.

$2.49