Question is here $$f(z) = \frac{|z-1|^4}{(z-1)^3} | (z\neq 1), f(1)=0$$
I have no idea how to partially differentiate a function with $|z-1|^4$ in the numerator and I can't find examples of similar problems with anything other than a final solution that doesn't make much sense.
Any help or first steps would be appreciated.
to show some work, I know that it's required to separate into u(x,y) and v(x,y), but I'm not sure how to separate the real and imaginary portion of the mod|z| without multiplying it all out. if I knew what u and v were I would have a solid grasp of where to go.