Complex Mapping Diagrams for Quadratic Function and Solving Real Quadratic Equations
Consider the complex quadratic function: first with .
By checking the box "Show mapping diagram:f with parameters B and C" you can see a mapping diagram in the 3D frame based on points chosen in a circle of radius centered on the point z#.
The point z# can be moved freely in the complex plane domain frame.
The slider n controls the number of points selected on the circle in the domain frame, while the slider controls the radius of the circle in the domain frame.
By checking the box "Show 3D graph of |f(z)|" you can see the cartesian 3D graph above the complex plane, showing the roots as points of contact between the graph surface and the complex plane.
By checking the box "show roots of quadratic equation" you can see the solution to the quadratic equation visualized with the mapping diagram as well as on the domain frame and on the real cartesian graph.
By moving the sliders Br and Cr you can change the real coefficients B and C for the function and observe the corresponding changes on the cartesian graph of , the values of its roots, and the mapping diagram.
By sliding the slider marked "complex or real " you can change the coefficient parameters Br and Cr to be complex numbers B and C in the domain frame. These complex numbers/points can be moved in the domain frame to change their values and explore further the related complex function and quadratic equation.