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Polynomials and Differentials: The Cauchy Riemann Equation

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** Please see the attached document for the complete problem description **
Please help solve this attached problem that involves polynomials and differentials. It involves an application of the Cauchy Riemann equation.

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Solution Summary

This solution contains a detailed 1.5 pages solution. The solution first briefly reviews the concept of Cauchy Riemann equations and then provides a step-by-step solution to the given problem using this concept.

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** Please see the attached file for the complete solution **
Write (please see the attached file). There by f is a polynomial, it is differentiable everywhere. It follows from Cauchy-Riemann equation that:
(please see the attached file)

Let us think about the function h, g as given. They are differentiable if, and only if, their corresponding real and imaginary part follows the Cauchy ...

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