Geometric Construction of the nth Roots of Unity on the Complex Plane

This GeoGebra example demonstrates the nth roots of unity as equally spaced points on the unit circle in the complex plane, illustrating how complex multiplication corresponds to rotation and how the roots form the vertices of a regular n-gon. Core mathematical concepts include complex numbers, roots of unity, trigonometric and polar representations, angle bisection, and regular polygon geometry. The construction employs GeoGebra commands such as Point, Intersect, Rotate, Angle, Ray, Segment, FractionText, AngularBisector, Midpoint, and SurdText, together with objects n, k, a, O, A, A′, α, z_k and related text labels to generate and annotate the roots. It is suitable for high school complex number electives, undergraduate complex analysis courses, and classroom demonstrations exploring the geometric and algebraic properties of roots of unity.