Consider the complex mapping w = z2.
(a) Do Problem for the mapping w = z2.
(b) Experiment with different rays. What effect does the complex mappingw = z2 appear to have on angles between rays emanating from the origin?
Problem
In this problem we investigate the effect of the mapping w = z2, where a is a complex constant and a ≠ 0, on angles between rays emanating from the origin.
(a) Let C be a ray in the complex plane emanating from the origin. Use parametrizations to show that the image C′ of C under w = z2 is also a ray emanating from the origin.
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