Complex Numbers: What's My Rule?

Points A, B, and C are complex numbers. Drag points A and B. Point C moves in response. What is the rule that defines points C? Try to describe it geometrically and algebraically. Is it possible to move A or B without moving C? Is it possible to move A or B so point C is at the origin? What happens to C when A is at the origin? What happens to C when B is at the origin? Is it possible to move A or B so point C moves along the Real axis? Is it possible to move A or B so point C moves along the Imaginary axis?