Points A, B, and C are complex numbers. Point A is constrained to the Real axis. 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?