Geometric Conversion of Complex Numbers: Cartesian to Polar

This example demonstrates how a single complex number is represented in the complex plane when switching from Cartesian coordinates to polar form. Visually, it relates the modulus r (distance from the origin) and the argument θ (rotation angle) to the same point z, making the equivalence between a+bi and r(cosθ + i sinθ) clear. The construction centers on key concepts: complex numbers on the complex plane, modulus and argument, angle measurement, and right-triangle/projection geometry. In GeoGebra, the build uses objects such as z and several auxiliary points/labels (e.g., a, b, r, θ, A, B, c, d, e, f, and text annotations) together with commands OrthogonalLine (to draw perpendicular aids), Intersect (to compute intersection points for the construction), Segment (to show the relevant geometric segments like radii/projections), and Angle (to display the argument θ). Suitable for high school to early university students, especially for introductory complex-number lessons, coordinate-geometry visualization, and trigonometry-based understanding.