Consider the complex quadratic function:[math]f(z)=z^2+Bz+C[/math] first with [math]B,C\in\mathbb{R}[/math]. [br][br]By checking the box "[b]Show mapping diagram:f with parameters B and C[/b]" you can see a mapping diagram in the 3D frame based on points chosen in a circle of radius [math]\delta[/math] centered on the point z[sub]#[/sub]. [br]The point z[sub]#[/sub] can be moved freely in the complex plane domain frame.[br]The slider [b]n [/b]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.[br][br]By checking the box "[b]Show 3D graph of |f(z)|[/b]" 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.[br][br]By checking the box "[b]show roots of quadratic equation[/b]" you can see the solution to the quadratic equation [math]f(z)=x^2+Bx+C=0[/math] visualized with the mapping diagram as well as on the domain frame and on the real cartesian graph.[br][br]By moving the sliders B[sub]r[/sub] and C[sub]r[/sub] you can change the real coefficients B and C for the function and observe the corresponding changes on the cartesian graph of [math]f[/math], the values of its roots, and the mapping diagram.[br][br]By sliding the slider marked "[b]complex or real[/b] " you can change the coefficient parameters B[sub]r[/sub] and C[sub]r[/sub] 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.