Vectors as Complex Numbers Applet 3a

This interactive GeoGebra applet demonstrates how to represent plane vectors as complex numbers, leveraging the algebraic and geometric properties of complex numbers for vector operations and angle measurement. Core mathematical concepts include the geometric representation of complex numbers (real part as x-coordinate, imaginary part as y-coordinate), the correspondence between vectors and complex numbers, vector addition and rotation (multiplication by a unit complex number), and the relationship between vector angles and arguments. Construction details: using GeoGebra commands such as Point, Circle, Vector, Segment, Intersect, and Angle, the applet constructs points R, A, B, C, circle c, vectors u and f, intersection points, and angle α, while defining complex numbers Z1 and z_{1}. Users can drag points dynamically to observe how vectors change. Suitable for high school or early university students learning the connection between complex numbers and vectors, and useful for teaching analytic geometry or trigonometry, particularly to visualize the geometric meaning of complex multiplication as vector rotation.