Geometric Representation of Analytic Functions

Extract

The study of the function of a real variable is aided by the " graph " of the function. Whenever difficult analytical notions are considered, such as continuity, turning points, etc., a study of the graph enables the student to get a general view of the problem.

No such help appears to be available in teaching the theory of functions of the complex variable. A " graph " of f(x + iy) = u + iv would require a fourdimensional space. Nevertheless some representation of an analytic function seems necessary if the student is not to be discouraged by the abstract nature of the idea.