Geometric Demonstration of Product and Quotient of Complex Numbers

① This example visualizes the geometric transformations corresponding to the product and quotient of complex numbers on the complex plane, showing how magnitudes multiply and arguments add for the product, and magnitudes divide and arguments subtract for the quotient. ② Core mathematical concepts include algebraic and polar forms of complex numbers, modulus and argument, geometric meaning of complex multiplication and division, and vector rotation and scaling. ③ Construction highlights: GeoGebra commands Intersect, Circle, PointIn, Vector, Point, Angle, Distance build the two complex points z₁, z₂ and their product z_P and quotient; polar objects Polar, angles θ₁, θ₂, distances distanceAz1, distanceAz2, and text labels text1…text14 dynamically display modulus and argument changes; a slider Show1 controls the demonstration steps. ④ Suitable for high‑school complex‑number units, introductory university complex analysis, and for teacher presentations or student self‑exploration.