Hey stuffthings.
If you can't show using Cauchy-Riemann, why not just use the definition of the derivative as a limit and show that the limit exists everywhere where it is differentiable.
Using the definition of the derivative find at which points the function f(z) = Im(z)/z conjugate is complex differentiable.
I know that it is not complex differentiable anywhere but I need to show it using the definition and not the Cauchy Riemann equations.