Take two quadratic functions whose graphs are congruent parabolas such that one opens up, the other down and they share a common vertex not on the xaxis.
Clearly one has two real roots, and the other two complex roots.
Discover a relationship between these roots.
The real component of each of the complex roots is the mean between the two real roots. The imaginary components are plus or minus i times half the difference between the two real roots.
The set of four roots altogether are the north, south, east and west compass points on a circle centered on the real axis of the Argand plane.

Posted by Charlie
on 20130325 16:53:46 