Complex Numbers: What's My Rule? – Explore the Relationship

This GeoGebra example presents an interactive exploration in the complex plane: points A, B, and C are complex numbers, and as you drag A and B, point C moves accordingly, inviting you to deduce the rule that defines C. The core mathematical concepts involve complex number operations (such as addition, multiplication, conjugation, or modulus) and their geometric interpretations, along with connections to function graphs, trigonometry, ratios, and straight lines. The construction uses simple point objects (A, B, C) with dynamic dependencies, allowing users to observe how C responds to changes in A and B. This activity is ideal for high school or early college students learning complex numbers, as well as for teachers seeking an inquiry-based demonstration to help students hypothesize and verify algebraic rules through visual experimentation.