captain black can you or someone else give me a hand to solve this problem. spent hours trying to do it but finding it very very difficult so if someone could help me would be really grateful and would really help my understanding
thanx in advance
(a) Verify that Im(z) and z do not satisfy the Cauchy-Riemann equations
at any point (so neither function is differentiable anywhere).
(b) Consider the function f(x+iy) = p|xy|, where x, y ∈ R. Show that
f satisfies the Cauchy-Riemann equations at the origin, yet f is not
holomorphic at 0.