Geometric Construction of the nth Roots of a Complex Number

This GeoGebra example demonstrates the geometric distribution of the nth roots of a complex number in the complex plane, showing how all n distinct nth roots are equally spaced around a circle centered at the origin with radius equal to the nth root of the original complex number's modulus. Core mathematical concepts include complex modulus, argument, De Moivre's theorem, roots of unity, and the rotational interpretation of complex multiplication. The construction uses GeoGebra commands such as Point, Intersect, Rotate, Angle, Ray, Segment, FractionText, AngularBisector, and Midpoint, together with objects like O, A, A′, α, r, B, C, z_k, n, and button1 to dynamically generate root points and annotate their coordinates or polar information. Suitable for high school elective mathematics or undergraduate complex analysis courses, this interactive applet supports classroom demonstration and independent inquiry into the geometric meaning of complex number operations.