MHB Complex function that satisfies Cauchy Riemann equations

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The discussion focuses on finding complex numbers z for the function f(z) = z cos(z̅), where z̅ is the complex conjugate. The original poster seeks guidance on deriving the partial differential equations related to the function, rather than determining where it is holomorphic. Participants clarify the intent of the inquiry, emphasizing the importance of differentiability in the context of complex analysis. The conversation highlights the need to understand the relationships between the real and imaginary parts of the function. Overall, the thread revolves around the application of the Cauchy-Riemann equations to this specific function.
beetlez
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Hi,
I am currently teaching myself complex analysis (using Stein and Shakarchi) and wondered if someone can guide me with this:

Find all the complex numbers z∈ C such that f(z)=z cos (z ̅).

[z ̅ is z-bar, the complex conjugate).

Thanks!
 
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Hi beetlez,

Just to be clear, are you looking to find all complex numbers $z$ at which $f$ holomorphic?
 
Euge said:
Hi beetlez,

Just to be clear, are you looking to find all complex numbers $z$ at which $f$ holomorphic?

Hi, no actually just assuming that the function is differentiable, I just wanted help to derive the partial differential equations (du/dx, du/dy, dv/dx and dv/dy).
 

Thread 'The Riemann'

1. Start with the global analytic continuation of the Riemann zeta function found here. 2. Form the Haadamard product. 3. Use the product to series formula from functions.wolfram.com or Theory and Applications of Infinite Series by Konard Knopp, Dover books 1943. 4. Apply series revision to solve for the zeroes from Stewart Calculus, 4th edition. Benjamin Orin and Leonard Mlodinow solved this.
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