Consider the function defined on the extended complex plane.
(a) Using the fact that h is a composition of the linear function g(z) = 2iz − 1 and the reciprocal function f(z) = 1/z, that is, h(z) = f(g(z)), describe in words the action of the mapping w = h(z).
(b) Determine the image of the line y = 1 under w = h(z).
(c) Determine the image of the circle under w = h(z).
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