Page "Holomorphic function" Paragraph 22

Every holomorphic function can be separated into its real and imaginary parts, and each of these is a solution of Laplace's equation on R < sup > 2 </ sup >.

In other words, if we express a holomorphic function f ( z ) as u ( x, y ) + i v ( x, y ) both u and v are harmonic functions, where v is the harmonic conjugate of u and vice-versa.