Quadratic Equation: Complex Roots
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Imagining Complex Roots
This example illustrates the real and complex roots of a quadratic equation. By observing the intersections of the quadratic function with the x-axis, the concept of real roots is understood. Further, through geometric transformations and complex numbers, the positions of complex roots can be visualized. The example uses commands such as Intersect, Mirror, Circle, and ComplexRoot, suitable for high school mathematics education.
GeoGebra Commands & Parameters
Intersect(f, xAxis) → A, BOrthogonalLine(P, xAxis) → dIntersect(f, d) → CMirror(f, C) → f_1Intersect(f_1, xAxis) → E, FCircle(P, F) → eIntersect(xAxis, yAxis) → GIntersect(e, d, 2) → HComplexRoot(f) → z_1, z_2Vector(G, z_1) → uVector(G, z_2) → v