Maximization Methods for Functions of a Complex Variable

The maxima and minima of a function of a real variable are found by equating to zero the derivative of the function. In the case of a function of a complex variable however the derivative is a vector quantity, so that conditions may be imposed upon its direction as well as upon its magnitude. These various conditions lead to maxima and minima of the various aspects of the function. Rules are developed for setting up equations giving the various maximizing conditions, and a simple example is given illustrative of the use of each rule.