Dynamic Visualization of Complex Integrals with Cabri II Plus

Abstract

Dynamic visualization helps us understand the concepts of mathematics very easily. This paper shows that of complex integrals with Cabri II Plus. The geometrical interpretation of complex numbers was introduced by Gauss using complex plane, but in general this geometrical idea has not been sufficiently made much of in the scene of education. This is only taught in the beginning, and is rarely used in teaching complex integration. Furthermore its dynamic visualization is hardly found out. And this is one of the most difficult fields for students, while it often appears in studying science. This paper highlights not only the visualization of mathematical concepts but also the effectuality of moving figures. Observing their movements makes it easier to find out mathematical properties. Cabri Geometry enables us to make moving figures without the knowledge of programming. Complex integrals are visualized with the idea of quadrature mensuration by parts, using the geometrical interpretation of the product of complex numbers; rotation and dilation. This dynamic visualization helps students understand complex integration deeply.