Abstract
Our purpose in this note is to illustrate the Cauchy integral formula and the concept of winding number. The software we use is fiz), ver. 4.0, Martin Lapidus, Lascaux Graphics, Bronx, NY, 1988. Many mathematicians and most students are at a loss to picture the graph of even the most elementary complex function. This tutorial and graphics program enhances geometric intuition about functions of a complex variable by graphing lines, circles, or other figures in a z plane and simultaneously graphing their images in a w =/(z) plane. Other domain options include hyperbolic lines on the Poincare plane and circles on the Riemann sphere. You can construct and save a page with two or more windows, sized, scaled, and positioned as you wish, and with domain options, functions, and operations specified. Once you have con? structed a page, you can request that the operations be carried out at the press of a draw key. The Cauchy integral formula states that
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