A computer graphics method for solving transcendental equations

There are a number of ways to determine the values of x which satisfy the equation F(x)=0. (The case of interest here is that in which F i s a complex function of the complex variable x.) One way is to search for values of x which make Real (F(x)) and Imaginary (F(x)) both zero at the same time where the search is based on sign changes in both quantities. There is a problem in that a sign change occurs across a pole as well as a zero.