# Complex Valued Funtions

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Define the complex-valued function of a complex variable f: C --> C by

f(z) = [IM(z)]^2

If S = {z is an element of C: Im(z) = 0} is the real axis, show using the definition of the derivative that f is differentiable at every z is an element of S. Show further that f is not differentiable elsewhere, ie. f is not differentiable at any z in C/S.

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#### Solution Summary

This solution shows how to solve the complex-valued function in an attached Word document.

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