Numerical solution methods for real conservative fields are abundant in the literature, but interest in complex potential problems has been very low. The author presents ideas that justify interest in complex scalar potentials. For instance, the ability to solve complex scalar potential problems is shown to be a prerequisite for the solution of general, three-dimensional, magnetic vector potential problems. As another example, the electromagnetic properties of dielectrics, semiconductors, and magnetic materials can be described by complex material property tensors. The electric or magnetic scalar potential distribution in such media may be obtained from the complex Laplace’s equation. The paper examines three-dimensional anisotropic complex potential problems and briefly describes a finite element formulation based on a brick-shaped, second-order, subparametric finite element. An example illustrates the method.