Complex Numbers: What's My Rule?

Points A and C are complex numbers. Drag point A. 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 without moving C? Is it possible to move A so point C is at the origin? What happens to C when A moves along the Real axis? What happens to C when A moves along the Imaginary axis? Is it possible to move A so point C moves along the Real axis? Is it possible to move A so point C moves along the Imaginary axis?

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