Finding Complex Roots: Visualizing Polynomial Zeros

① This GeoGebra example dynamically displays the complex roots of a polynomial equation on the complex plane, making their positions and distribution visually intuitive. ② Core mathematical concepts include complex numbers, polynomial root-finding, the Fundamental Theorem of Algebra (an n-degree polynomial has n complex roots counting multiplicities), and the geometric representation of the complex plane with real and imaginary axes. ③ Construction highlights: The Sequence command is used to generate a sequence of roots, with objects such as target, n, principal, and roots computing and displaying all roots; text1 and text2 annotate the root values or explanatory notes, resulting in a scatter plot of roots on the complex plane. ④ This is suitable for upper high school or early university mathematics, helping students grasp the existence of complex roots, the pairing of conjugate roots, and the connection between roots and polynomial factorization, as well as exploring how coefficient changes affect root locations.