Geometric Representation of Complex Zeros of Quadratic Functions

This GeoGebra example demonstrates how to visually represent complex roots of quadratic functions on the complex plane. By inputting coefficients for a quadratic function, the applet plots the function graph and uses complex number tools to find its conjugate complex zeros. Core mathematical concepts include: quadratic formula, geometric representation of complex numbers (conjugate symmetry), complex modulus and argument. Construction uses: Line command for coordinate axes, Mirror command to reflect zeros across the real axis to obtain conjugate complexes, Rotate command to illustrate argument relationships. Objects include: a, b, c as quadratic coefficients, f as function graph, A, B as zero points, d, e as auxiliary lines, g, h as transformed geometric elements. Suitable for high school or pre-university students learning complex numbers and their geometric interpretations, as well as teachers demonstrating the geometric meaning of complex roots.