According to the Maximum Modulus Principle, must be constant in so with .
I have the following question:
A complex function f is differentiable in a region and satisfies the equation for all . Determine the function f.
I started by saying . We know .
And we know also the Cauchy-Riemann equations since f is differentiable. I tried taking derivatives in but I was stuck. An intuitive function to have is where c is a complex number with magnitude 1.
Any help is appreciated.