1. The problem statement, all variables and given/known data f(z) = u(x, y) + iv(x, y) where z ≡ x + iy. Let the ﬂuid velocity be V = ∇u. If f(z) is analytic, show that df/dz = V_x − iV_y 2. Relevant equations V_x = du/dx V_y = idu/dy The CR equations du/dx = dv/dy, du/dy = -dv/dx. 3. The attempt at a solution I attempted to use this form for d/dz: d/dz = d/dx - i*d/dy. This gave me df/dz = 2(V_x - iV_y) though.