Visualizing Complex Roots of Quadratic Functions

This example demonstrates how to find roots of quadratic equations in the complex number domain and visualize their distribution on the complex plane. Key mathematical concepts include the quadratic formula, geometric representation of complex numbers, and the relationship between roots and coefficients. Construction: Use the Root command to solve for complex roots, CurveCartesian to plot points on the complex plane, Solutions to obtain all equation solutions, and rp/ip to extract real and imaginary parts. Roots are color-coded to distinguish real roots from conjugate pairs. Suitable for high school advanced mathematics or pre-university students learning complex numbers and their geometric properties, particularly for understanding conjugate symmetry when discriminant Δ<0.