A function f = u + iv is holomorphic iff u_x = v_y and u_y = −v_x (and u, v are differentiable). Holomorphicity = a pair of PDEs on the real and imaginary parts.
A function f = u + iv is holomorphic iff u_x = v_y and u_y = −v_x (and u, v are differentiable). Holomorphicity = a pair of PDEs on the real and imaginary parts.