Geometric construction to introduce the imaginary unit i

This GeoGebra practice introduces the imaginary unit i by building a visual number–shape correspondence. It demonstrates how constraints from geometry—such as circumcircle/circumscribed-circle style configurations and ellipse-related loci—can encode algebraic ideas behind complex numbers. The core concepts include complex numbers (especially the role of i), vector/coordinate representations of geometric quantities, and how set-theoretic/geometric constraints lead to invariant structures on the plane. In the construction, key objects b, a, c, d, e, f, h, g are used to define base points and the relationships among them: first, establish the foundational geometric configuration (e.g., circles or circle-related constructions implied by the chosen points), then introduce intermediate points (d–h) to represent algebraic steps such as taking arithmetic means and enforcing length/equality/orthogonality-type constraints. As a result, i is not treated purely as a symbol, but as a feature with a concrete geometric manifestation. Suitable for upper-secondary to early university learners and for classroom demonstrations focused on complex numbers and dynamic geometry construction.