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    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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    https://brainmass.com/math/complex-analysis/calculus-transformation-complex-numbers-315652

    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.

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