Lectures related to Complex Numbers: Roots and Polynomials

Complex Roots and Polynomials

Explores complex roots, polynomials, and factorizations, including roots of unity and the fundamental theorem of algebra.

The Fundamental Theorem of Algebra

Covers the fundamental theorem of algebra, explaining how every polynomial has complex roots.

Complex Numbers: Operations and Applications

Explores complex number properties, roots, and polynomial equations in the complex plane.

Factorisation: Polynomials and Theorem

Covers irreducible polynomials, fundamental theorem of algebra, and factorization in complex and real polynomials.

Polynomials: Definitions and Operations

Covers the definition and operations of polynomials, including addition and multiplication, degree, coefficients, and their role in algebraic systems.

Factorisation: Real Coefficients Examples

Covers the factorization of polynomials with real coefficients in the complex domain, demonstrating how to find complex roots and obtain irreducible factors.

Complex Polynomials and Factorization

Explores complex polynomials, factorization, roots of equations, equilateral triangles, and infinite sums in sequences.

Polynomials with Real Coefficients

Explores polynomials with real coefficients, complex roots, and sequences' properties.

Integration on H_pxH and Arithmetic

Explores integration on H_pxH and arithmetic properties, including norms, structures, and polynomial factorization.

Complex Roots: Conjugate Pairs and Quadratic Equations

Explores complex roots, conjugate pairs, and quadratic equations solving strategies.

Polynomials and Endomorphisms

Covers the fundamentals of polynomials, endomorphisms, division, roots, matrices, and algebraic homomorphisms.

Fundamental Theorem of Algebra

Covers the Fundamental Theorem of Algebra, complex sequences, convergence, and continuity of functions.

Complex Numbers: Polar Form

Covers the polar form of complex numbers and its applications in mathematical calculations.

Integration: Simple Elements

Covers the integration of simple elements using various techniques to solve integration problems.

Complex Plane and Polynomials

Covers the complex plane, operations, transformations, and complex polynomials.

Complex Factorization Examples

Explores complex polynomial factorization examples, demonstrating the process and implications of complex roots in real polynomials.

Applications of Residue Theorem in Complex Analysis

Covers the applications of the Residue theorem in evaluating complex integrals related to real analysis.

Polynomials on a Field: Basics and Operations

Introduces the basics of polynomials on a field, focusing on definitions, operations, and properties.

Linear Combinations and Vector Spaces

Introduces linear combinations in vector spaces, operations, and polynomials of degree 2.

Differentiable Functions and Lagrange Multipliers

Covers differentiable functions, extreme points, and the Lagrange multiplier method for optimization.