Locus of Points from Modulus Equation |z-a|=n|z-b|

This GeoGebra example dynamically demonstrates the locus of points generated by the complex number equation |z - a| = n|z - b|. As the parameter n varies, the set of complex numbers z satisfying the equation traces a curve on the complex plane, revealing the geometric meaning of a constant ratio of distances to two fixed points. Core mathematical concepts include the modulus of complex numbers, distance between points, the Apollonius circle (when n≠1 the locus is a circle, and when n=1 it becomes a line), and locus equations. Construction details: using basic commands such as Segment, Point, and Ray to define points a, b, and a moving point P; a slider controls the parameter n; distances d_1 and d_2 are measured to verify the equation; and the locus tool generates the final curve g. This is suitable for high school or early college students learning the geometric interpretation of complex numbers, as well as for teaching locus problems in analytic geometry.