Determine the cauchy-riemann equations

Question

Cauchy-Riemann Equations

1. Let u and v denote the real and imaginary components of the function f defined by the equations
  
  f (z) = z¯²/z when z ≠ 0,

  f (z) = 0  when z = 0,

Verify that the Cauchy-Riemann equations ux = vy and uy = -vx are satisfied at the origin z = (0, 0).

Provide step by step calculations.