A holomorphic function is a complex function that is complex differentiable on every point in its domain; that is, the derivative exists and the power series converges. A complex function f(z) will be holomorphic iff If a function is holomorphic it will obey the Cauchy–Riemann conditions (and by extension, Laplace's equation). If a function obeys the Cauchy-Riemann conditions and the derivative is not zero, it will also preserve angles, and so will be holomorphic if the other two conditions are met. All holomorphic functions are also analytic.