Assess understanding of Newton's method applied to complex polynomials by asking learners to analyze local and global convergence properties, classify stability of simple and multiple roots, determine rates of convergence, characterize basins of attraction and their boundaries (including relation to Julia sets), and evaluate sensitivity to initial conditions and parameter perturbations through proofs, analytical criteria, and targeted numerical/graphical experiments. Scope: complex dynamics of iterative maps for polynomials, root multiplicity, and basin topology.