Simple determination via complex arithmetic of geometric characteristics of Bézier conics

We show how to compute in a straightforward manner the geometric characteristics of a conic segment in rational Bézier form, by employing complex arithmetic. For a central conic, a simple quadratic equation defines the foci location, and its solution furnishes not only an explicit formula for the foci, but also for the center, axis direction and linear eccentricity.

► Complex arithmetic simplifies formulae for characteristic of conics in Bézier form.
► For central conics, a complex quadratic equation defines the foci location.
► The solution also furnishes the center, axis direction and linear eccentricity.
► For a parabola, the equation characterizing the focus degenerates to a linear one.