Cauchy-Riemann equation

noun2

1. •
   Given a complex-valued function f and real-valued functions u and v such that f(z) = u(z) + iv(z), either of the equations (∂u)/(∂x)=(∂v)/(∂y) or (∂u)/(∂y)=-(∂v)/(∂x), which together form part of the criteria that f be complex-differentiable.
2. •
   The equivalent single equation (∂f)/(∂x)+i(∂f)/(∂y)=0.