Abstract: This paper presents an extended instructional example that ties together many of the concepts often encountered in college algebra. The original goal for the example was to find an application in which polynomial equations of arbitrarily high degree arise naturally, but the example has acquired other virtues over the years. In its present form, it serves as a convenient and unified review of such diverse topics as Descartes' Rule of Signs, Geometric Series, exponential functions and complex numbers, as well as a good illustration of the power of symbolic math software such as Mathematica.