Complex Roots and Polynomials

This lecture covers the concept of n-th roots of complex numbers, polynomials with complex and real coefficients, and factorizations. It explores the properties of roots, including translation-invariant kernels and quadratic problems. The instructor demonstrates examples of roots of unity and solutions to polynomial equations using polar form. The lecture concludes with a discussion on the fundamental theorem of algebra, factorization of real polynomials, and the discriminant complex. Various examples illustrate the factorization of polynomials with real and complex coefficients.