Real Transformations from Complex Numbers.

In this article we shall investigate the transformations that result when all varia bles and constants in these functions are al lowed to be complex numbers. Although complex numbers are used to obtain the transformation equations, the transforma tions themselves can be described and studied without any mention of complex numbers. It is hoped, therefore, that this material may be useful for many high school students. However, it is essential to provide them with copies of the grids that are illustrated on the following pages. It is necessary to establish the following conventions at the outset. Complex varia bles will be represented by