Complex Numbers: Algebraic and Trigonometric Form with Geometric Representation

This GeoGebra example demonstrates the conversion between the algebraic form (a+bi) and trigonometric form (ρ(cosθ + i sinθ)) of a complex number, along with its geometric representation in the complex plane. It visually shows the modulus (ρ), argument (θ), and the corresponding vector from the origin to the point representing the complex number. Core mathematical concepts include real and imaginary parts, modulus, argument, polar coordinates, and the geometric interpretation of complex numbers. The construction uses GeoGebra commands such as Textfield for input boxes, Vector to draw the complex vector, Point to mark key locations (origin O and point A), Angle to display the argument θ, and Segment for connecting lines. Dynamic text and sliders update values in real time. This resource is suitable for high school or introductory college students learning complex numbers, and serves as an effective classroom demonstration tool for teachers.