# To find the analytic function f(z) = u + iv when u is given.

Functions of a Complex Variables

Analytic Functions

If u = sin x . cosh y + 2cos x . sinh y + x2 - y2 + 4xy ,

then prove that u is a harmonic function and find the analytic function f(z) = u + iv .

See attached file for full problem description.

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#### Solution Summary

This solution is comprised of a detailed explanation for harmonic function and finding the analytic function f(z) = u + iv.

It contains step-by-step explanation for the following problem:-

If u = sin x . cosh y + 2cos x . sinh y + x2 - y2 + 4xy ,

then prove that u is a harmonic function and find the analytic function f(z) = u + iv .

Solution contains detailed step-by-step explanation.

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