Locus of Points from Modulus of Complex Numbers: |z-a| = n|z-b|

This GeoGebra example dynamically illustrates the locus of points z in the complex plane satisfying |z-a| = n|z-b|, where a and b are fixed complex numbers and n is a positive real parameter. When n=1, the locus is the perpendicular bisector of segment ab; when n≠1, it becomes an Apollonius circle. The core mathematical concepts include the modulus of complex numbers, distance ratios, locus equations, and the geometric relationship between circles and lines. Construction details: using GeoGebra commands Segment, Point, and Ray to build the base figure, defining complex objects z_1, z_2 and parameter n, controlling n with a slider, generating the locus of point P via the Locus tool, and displaying distances d_1, d_2 along with their ratio text. This is suitable for high school or early college students to explore the geometric meaning of complex numbers, investigate properties of Apollonius circles, or serve as dynamic teaching material combining analytic geometry and complex analysis.