Complex Numbers: What's My Rule? by Carolijn Tacken
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This interactive GeoGebra sheet displays three points A, B and C on the complex plane. Drag points A and B and watch point C respond; the goal is to discover the rule that defines C in terms of A and B. It demonstrates complex numbers as vectors, coordinate geometry, and the concept of a locus, while requiring the use of the Point command to create the points and complex‑number operations to generate C. Suitable for high‑school or early‑undergraduate students learning about complex numbers, vectors and geometric relationships.
GeoGebra Commands & Parameters
Point(xAxis) → A
AI Drawing Prompt Reference
Draw a complex plane with three points, where two points are draggable and the third is determined by a complex-number operation on the first two. Place one point on the real axis, another anywhere in the plane, then compute the third point's position based on their relationship (such as addition, multiplication, or conjugation). As you drag the first two points, the third moves accordingly, tracing a locus. Show coordinate axes, grid, and label the points with their coordinates to help discover the rule.
The prompt above was compiled from the original drawing commands and is for reference only.