Fundamental Theorem of Algebra

This lecture covers the Fundamental Theorem of Algebra, stating that every equation of the form anzn + an-1zn-1 + ... + a1z + a0 = 0 has a solution in the complex numbers. It also discusses the properties of complex sequences, convergence, and continuity of complex functions. The lecture presents preparatory theorems and their proofs, leading to the conclusion of the Fundamental Theorem of Algebra. The proofs involve analyzing polynomial functions, infimum of sets, and the existence of complex numbers satisfying specific conditions.