Experiments you can run yourself.
Multiplying a complex number by i corresponds to a 90° rotation in the plane.
e^(iπ) = −1, giving Euler's identity e^(iπ)+1=0, which ties together five constants: e, i, π, 1, 0.
There is no general formula for the roots of a fifth-degree equation (unlike the discriminant for the quadratic).
The number of solutions of a system equals the number of points the two lines share.
The sign of the trinomial ax²+bx+c depends on the sign of a and the value of Δ.