Complex function that satisfies Cauchy Riemann equations

[beetlez]

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!

 

[Euge]

Hi beetlez,

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

 

[beetlez]

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).