Dynamic
Visualization of Complex Integrals with Cabri II Plus
Sae MIKI
sand_picture@hotmail.com
IES
Japan
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.
