Complex Mappings of a Line

This GeoGebra example demonstrates how a straight line in the complex plane transforms under various complex mappings. By dragging the red points, users can explore the images of the line under operations such as translation, rotation, scaling, and reflection, revealing the geometric nature of complex functions. Core mathematical concepts include complex numbers, complex-plane geometry, similarity transformations (conformal mappings), reflection, and continuity. The construction uses the Line command to define the original line, Point objects as draggable controls, and Locus to trace the mapped images. Key objects include D, C, d, a, b, Z, u, v, w, and text labels. This is suitable for high school or early university students learning the geometric interpretation of complex numbers, linear transformations, and locus problems, and serves as an interactive teaching tool for visualizing algebraic-to-geometric connections.