Geometric explanation of e^{i} using limits in the complex plane

This example visualizes how a limit-based explanation connected to e^{iθ} can be understood geometrically in the complex plane. It highlights the continuity behavior of the complex exponential: as a parameter varies toward its target value, the corresponding construction (especially the phase/angle information) converges, producing a consistent geometric picture. Key concepts include complex numbers via polar form, the complex extension of the exponential function (Euler-type rotation: e^{iθ}), continuity, and the role of limits in preserving geometric structure under refinement. Construction-wise, the GeoGebra setup uses commands such as Segment and Angle together with objects n, z_1, c, a, A, f, B, g, α, β, and z_2. Segments are used to build the relevant geometric relations, while Angle measures phase angles (α, β) that connect the plotted complex points z_1 and z_2 to the underlying exponential/rotation interpretation. Suitable for upper-secondary through early undergraduate audiences for teaching complex numbers, functions, and intuitive limit/continuity reasoning through visualization.