Exploring Complex Number Roots with Rotation

This GeoGebra example demonstrates how the n-th roots of a complex number are arranged in the complex plane. Given a complex number z, its n roots appear as equally spaced points around the origin, forming the vertices of a regular polygon. The main mathematical concepts include complex numbers, the complex plane, modulus, argument, roots of complex numbers, rotation, symmetry, and polygonal structure. In the construction, the Point command is used to create complex points or root points, while the Rotate command generates adjacent roots by rotating through 360°/n. Objects such as n, A, Complex, z_1 through z_10, LEdge, REdge, and text labels help display the roots, edges, explanations, and answers, making it easier to observe angular spacing and side relationships. This example is suitable for high school mathematics, pre-university courses, or introductory complex analysis, especially for exploring the geometric meaning of complex roots and verifying rotational symmetry through dynamic construction.