Lectures related to Complex Numbers: Equations and Constructibility

Polynomials: Definitions and Operations

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

Complex Numbers: Operations and Applications

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

Complex Roots and Polynomials

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

Intersection Numbers: Algebraic Counting Solutions

Explores intersection numbers for counting solutions to polynomial equations algebraically and their geometric significance in intersection theory and enumerative geometry.

Roots of n-th Degree

Covers the concept of roots of n-th degree in complex numbers and their exact solutions.

Sequences: Definitions and Examples

Covers solving equations over complex numbers, sequences, induction, and properties of complex numbers.

Complex Numbers: Gauss-Wantzel Theorem

Covers the Gauss-Wantzel Theorem and Fermat prime numbers.

Complex Polynomials and Factorization

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

Complex Numbers: Definitions and Applications

Explores complex numbers, arguments, modules, and polynomial equations with complex coefficients.

Polynomial Roots: Finding Solutions and Division

Explains how to find solutions for polynomial equations and perform polynomial division.

Complex Numbers: Operations and Applications

Covers the properties and operations of complex numbers and their applications.

Complex Numbers: Introduction and Properties

Covers the introduction to complex numbers and their properties, including historical background and norm calculation.

Tests of Invariance in Polynomial Equations

Explores testing invariance in polynomial equations, emphasizing solution identification and variable changes.

Factorisation: The Fundamental Theorem of Algebra

Covers the Fundamental Theorem of Algebra, polynomial division, and complete factorization of complex polynomials.

Complex Numbers: Operations, Polar Form, and Solutions

Covers operations on complex numbers, polar coordinates, and polynomial solutions.

Square Roots and Complex Numbers

Explores square roots in quadratic equations, complex numbers, Fermat prime numbers, and the Gauss-Wantzel theorem.

Complex Numbers: Group Morphisms and Fermat Primes

Explores group morphisms in complex numbers and the concept of Fermat primes.

Polynomial Equations: Solving Methods

Covers various methods for solving polynomial equations through examples.

Polynomial Equations: Determining Coefficients

Covers the process of determining coefficients in polynomial equations.

Complex Roots: Conjugate Pairs and Quadratic Equations

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