Cartesian Representation of Complex Numbers: Vector Visualization

① This GeoGebra example dynamically illustrates the Cartesian (rectangular) representation of complex numbers on the complex plane, showing a complex number a+bi as a vector from the origin with projections on the real and imaginary axes. ② The core mathematical concepts include the algebraic form of complex numbers, the complex plane, real and imaginary axes, and the correspondence between complex numbers and 2D vectors, aiding comprehension of the geometric meaning of complex arithmetic. ③ Construction highlights: using GeoGebra's Vector command to draw the complex vector, Segment command to construct the projection segments for real and imaginary parts; involved objects include complex point Z, vector u, auxiliary functions f and g, parameter a, and point A—dragging parameter a dynamically changes the real and imaginary parts, updating the vector. ④ Suitable for high school and early college students learning complex numbers, for classroom demonstration or self-study, and as a reference for teachers creating interactive complex-number teaching materials.