Visualizing Roots of Unity: Rotation and Powers on the Complex Plane

This GeoGebra example visualizes the roots of unity—the n complex solutions to z^n = 1—as equally spaced points on the unit circle in the complex plane. It demonstrates how multiplying by a root corresponds to rotation, and how raising a complex number to a power relates to its polar form. Core concepts include complex numbers, the unit circle, argument (angle), rotation, and Euler's formula. The construction uses commands such as Intersect, Circle, Rotate, Angle, ToComplex, ToPolar, and Vector, with objects like root, A, c, C, Nroot, α_1, u, v, power, NrootPower, w, z, β_1, and dynamic text showing expressions like "1 to the β power = 1^{1/...}". Suitable for high school or undergraduate students exploring complex analysis, trigonometry, or abstract algebra, and ideal for interactive classroom demonstrations or self-paced mathematical discovery.