4. Locus of the Solutions of a Complex Quadratic Equation

This Demonstration constructs the locus of the solutions of a complex quadratic equation , where is fixed and moves along a line through and .

The locus is an algebraic curve of degree three. Special cases are the union of a circle and a line or a line and a point. If is a positive real number and moves on the vertical line through , the locus is a strophoid.