A Complex-Number Based Construction of a Rectangle

This GeoGebra example demonstrates how to construct a “complex-formulated rectangle” in the plane by encoding geometric relationships with complex numbers and vector-like constructs. The key ideas are: using complex numbers to represent points/offsets algebraically, enforcing rectangle structure via geometric constraints, and locating vertices via intersections. Construction-wise, it relies on Intersect to compute critical intersection points, Segment to build the necessary lines/edges used in the construction, and Polygon to connect the resulting vertices into a closed rectangle. The scene includes multiple complex parameters/variables (z1, z2, z3, z4, …), vector-like objects (v1, v2), auxiliary lines/segments, and annotation texts (e.g., Text1). Suitable for high school to early university learners, especially for teaching the bridge between complex-number representations and classical Euclidean geometry construction.