Multiplying and Dividing Complex Numbers: Geometric Visualization

This GeoGebra example dynamically illustrates the geometric meaning of multiplication and division of complex numbers, showing how the modulus and argument change when two complex numbers are multiplied or divided. Core mathematical concepts include polar representation of complex numbers, modulus and argument, multiplication (moduli multiply, arguments add), division (moduli divide, arguments subtract), and vector operations on the complex plane. Construction highlights: uses the Intersect command to create intersection points, Segment command to draw segments, and defines complex objects z_1, z_2, z_3, z_4 with auxiliary objects α, β, text1, text2 to label angles and values, points A, f, g, h, i to build geometric relationships, and sliders or dynamic interactions to show results. Suitable for high school and above to grasp the geometric essence of complex arithmetic, and useful for university introductory complex analysis or classroom demonstrations.