ABSTRACT
We have already observed that, if f(z) is analytic in a domain D, then Re(f(z)) and Im(f(z)) are both harmonic functions; that is, they are both solutions of the Laplace equation. This is a direct consequence of the CauchyRiemann equations and of the fact that f(z) and hence Re(f(z)) and Im(f(z)) possess higher-order derivatives.
