Powers of 1+i: Visualizing Rotation and Scaling

This GeoGebra example visualizes the geometric meaning of powers of the complex number (1+i) from the 1st to the 8th power. On the complex plane, each power corresponds to a vector that rotates by 45° and scales by √2 relative to the previous one, forming a spiral polygonal path that clearly demonstrates the rotation-and-scaling nature of complex multiplication. Core mathematical concepts include polar representation of complex numbers, De Moivre's formula, vector operations, similar triangles, and geometric sequences. Construction details: using GeoGebra commands Intersect, Vector, and Point, points A, B, u, C, v, D, etc. are constructed sequentially, where each new point is obtained by multiplying the previous vector by (1+i), with text1 through text9 labeling the coordinates of each power. Suitable for high school and above to grasp the geometric intuition of complex arithmetic, and also useful for introductory complex analysis courses or teacher demonstrations.