Finding an Analyitic Function given Re(z)

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In summary, the conversation discusses finding a function that is analytic in a certain part of the Argand diagram and satisfies the Cauchy-Reimann relation. The individual has taken the derivative with respect to x and y and is attempting to integrate them to find an imaginary part of the equation. However, there is an integral that they are unsure how to solve.
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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?
 

FAQ: Finding an Analyitic Function given Re(z)

What is an analytic function?

An analytic function is a mathematical function that is defined and continuous for all values of a complex variable. It also has a unique derivative at every point in its domain.

How do you find an analytic function given Re(z)?

To find an analytic function given Re(z), you can use the Cauchy-Riemann equations. These equations relate the real and imaginary parts of a complex function and can help determine the form of the function.

Can an analytic function have a real or imaginary part equal to zero?

Yes, an analytic function can have a real or imaginary part equal to zero. However, this does not necessarily mean that the function itself is equal to zero.

Are all analytic functions also holomorphic functions?

Yes, all analytic functions are also holomorphic functions. Holomorphic functions are complex-valued functions that are defined and differentiable on an open subset of the complex plane.

What is the importance of finding an analytic function given Re(z)?

Finding an analytic function given Re(z) can help in solving a variety of mathematical and scientific problems, such as finding the maximum and minimum values of a function, solving differential equations, and understanding the behavior of complex systems.

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