Visualizing Roots of Complex Numbers: Equilateral Triangles on the Unit Circle

① This GeoGebra example dynamically illustrates the geometric meaning of taking the nth roots of a complex number: the n roots are evenly spaced on a circle centered at the origin with radius equal to the modulus, forming the vertices of a regular n-gon. ② Core mathematical concepts include polar representation of complex numbers (modulus and argument), De Moivre's theorem, roots of unity, and the connection between regular polygons and the complex plane. ③ Construction highlights: LaTeX and Textfield are used to create input boxes (InputBox1, InputBox2, InputBox3) for entering the real part, imaginary part, and root order n; the Sequence command generates the root sequence list1 for k from 0 to n-1; Intersect and Circle are used to construct the unit circle and intersection points, displaying each root as point A and connecting them to form equilateral triangles when n=3. ④ Suitable for high school to early college students to gain geometric intuition for complex arithmetic, and for math lab or inquiry-based learning to master the rules of complex root extraction from both algebraic and geometric perspectives.