Exploring the iteration of x² from complex numbers

This example iteratively applies the function x² starting from various complex numbers to investigate whether the resulting sequence remains bounded or diverges. By setting an initial complex value a, the GeoGebra commands IterationList and Sequence generate the terms of the series, while Circle and Intersect are used to plot the trajectory in the complex plane. The core mathematical ideas involve complex arithmetic, convergence of iterative functions, and geometric representation in the complex plane. It is intended for high‑school or early university students studying complex numbers and dynamical systems, and can serve as a tool for exploratory learning and mathematical modeling.