Finding an Analyitic Function given Re(z)

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SUMMARY

The discussion focuses on finding an analytic function f(z) where Re(z) is defined as sin(2x)/[cosh(2y)-cos(2x)]. The user, Andrew, attempts to derive the imaginary part of the function by applying the Cauchy-Riemann equations, specifically du/dx = dv/dy and du/dy = -dv/dx. However, he encounters difficulties in integrating the derived expressions. A suggestion is made to correct the expression for du/dy to facilitate easier integration.

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Homework Statement



Find a function f(z) that is analytic in a suitable part of the Argand diagram for which

Re(z) = sin(2x)/[cosh(2y)-cos(2x)]



The Attempt at a Solution



I've taken the derivative with respect to both x and y and am attempting to integrate them to find an imaginary part of the equation that will satisfy the Cauchy-Reimann relation (du/dx = dv/dy; du/dy = -dv/dx where u is Re(z) and v is Im(z)), but I et to an integral I am not sure how to solve. My work is attached in a scanned document.

Thanks for helping!
Andrew
 

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Your expression for du/dy would be a lot easier to integrate dx if it were correct. Can you fix it?
 

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