This equation represents the set of points in the complex plane that are equidistant from two distinct points: the point on the real axis and the point on the imaginary axis. Such conditions often describe a geometric locus, specifically a perpendicular bisector of the segment connecting these two points, forming a straight line.

To solve for , we can rewrite the equation as . Expanding both sides will lead to a quadratic equation in terms of and help us identify exactly where those distances match up. Remember, breaking the complex number into real and imaginary components can significantly aid in visualizing and finding solutions efficiently!