Rotating and Scaling a Rectangle with Complex Numbers

This GeoGebra example demonstrates how multiplying a rectangle ABCD by a complex number rotates it about the origin and scales it by the modulus of that number. It connects complex multiplication with geometric transformations, modulus and argument, rotation, dilation, and coordinate-plane interpretation. The construction uses Polygon to create the original rectangle poly1 and the transformed rectangle poly2, Point to define vertices A, B, C, D and E, F, G, H, Intersect for auxiliary positioning, Angle and Distance to measure the rotation angle alpha and distances such as |z|, and LaTeX/TextIz to display the complex number z and explanatory labels. It is suitable for high-school complex numbers, analytic geometry, and geometric transformations, as well as introductory college-level visualization of complex maps.