With possible exceptions in quantum mechanics, measurable physical quantities do not involve complex numbers. However, most standard and special functions in the applied sciences are analytic functions. Focusing on exact mathematical techniques, a famous quote notes that ‘The shortest path between two truths in the real domain passes through the complex domain’. It therefore becomes natural to ask if this shortest path can benefit from finite difference formulas and numerical quadrature methods that are specifically designed for the complex plane. Several such opportunities have recently been found. While the concepts of complex variables and of analyticity do not readily generalize beyond 2-D, the new numerical methods that are described here can be adapted to harmonic functions in higher dimensions.
