Geometric explanation of the e^{ix} power series (complex numbers)

This example visualizes the relationship between the complex exponential e^{ix} and its power-series expansion by building a geometric/complex-plane construction that shows how partial sums accumulate toward the target value. The key ideas are complex numbers, the meaning of e^{ix} for angles, and the power series viewpoint (Euler-formula intuition connecting complex exponentials with trigonometric behavior). Construction-wise, it uses the GeoGebra command “Segment” to draw a polyline formed by points z_1 through z_10, representing successive terms or partial sums in the series. Additional objects A, B, and C serve as reference points, while labeled objects f, g, h, i, j, k, l, m, n, p, q organize the intermediate quantities or geometric components used to place those points in the complex plane. The step-by-step, term-by-term geometry makes it suitable for learning, classroom demonstration, and early university preparation for complex analysis or advanced calculus.