A graphical method is described for finding the complex roots of a nonlinear equation: g( ω) = 0. Basically a mesh of potential roots, ω, is chosen; values of g on this mesh are calculated; and the zero contours of Re( g) and Im( g) are plotted. The intersections of these contours are the desired roots, or possibly singularities. The primary advantage of the method is that it provides the complete spectrum of roots or eigenvalues within a specified range of ω-space. The method is easy to apply, provided a reliable contour plotting routine is available, and is quite, efficient whenever g is inexpensive to evaluate. Application of the method is illustrated by two example problems from plasma physics.