Consider the function  defined on the extended complex plane.(a) Using the fact that h is...

Consider the function  defined on the extended complex plane.

(a) Using the fact that h is a composition of the reciprocal function f(z) = 1/z and the linear function g(z) = 2iz + 1, that is, h(z) = g(f(z)), describe in words the action of the mapping w = h(z).

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(b) Determine the image of the line x = 4 under w = h(z).

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(c) Determine the image of the circle |z + 2| = 2 under w = h(z).