Lectures related to Definition of Complex Numbers Field

Complex Numbers: Operations and Representations

Explores complex numbers, their operations, and representations in Cartesian and polar forms.

Complex Numbers: Introduction and Properties

Introduces complex numbers to solve unsolvable equations, exploring their properties and relationship with real numbers.

Linear Equations and Matrices: Solution Methods, Elementary Operations MOOC: Warm-up for EPFL MOOC: Linear Algebra (Part 1)

Explores solution methods and elementary operations for linear equations and matrices, demonstrating techniques to simplify systems and obtain solutions.

Elementary Properties of Complex Numbers

Covers the elementary properties of complex numbers and how to find real and imaginary parts.

Elementary Properties of Complex Numbers

Covers the elementary properties of complex numbers through examples and discusses the regions of the complex plane.

Complex Numbers: Cartesian Representation MOOC: Analysis I MOOC: Analysis I (part 2) : Introduction to complex numbers

Covers the Cartesian representation of complex numbers and basic operations involving them.

Complex Numbers: Properties and Operations

Explores complex numbers, Euler's formula, Moivre's formula, and proof by induction.

Element Inverse for Multiplication MOOC: Analysis I MOOC: Analysis I (part 2) : Introduction to complex numbers

Covers the concept of element inverse for multiplication in complex numbers.

Complex Numbers: Definition

Covers the construction and properties of complex numbers, introducing the new constant 'i'.

Complex Numbers: Module and Conjugate

Covers the manipulation of algebraic laws on complex numbers.

Analyse I: Summary

Covers real numbers, complex numbers, numerical sequences, series, real functions, function limits, derivatives, Taylor series, integrals, and growth rates of functions.

Power Series Computations

Covers power series, generating functions, and operations like addition, multiplication, differentiation, and integration, with examples and the generalized binomial theorem.

Complex Roots: Conjugate Pairs and Quadratic Equations

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

Setting up arithmetic

Explores defining arithmetic operations through counting, with insights on cardinal numbers, Cantor's work, and Sudoku.

Linear Algebra in 3D: Matrices and Determinants

Covers linear algebra in three dimensions, focusing on matrices and determinants.

Modular Arithmetic: Operations and Polynomials

Covers modular arithmetic operations and polynomial calculations modulo N with various examples.

Algebraic Operations MOOC: Analysis I (part 1): Prelude, basic concepts, real numbers MOOC: Analysis I

Covers the basic concepts of rational numbers and algebraic operations, including addition, subtraction, multiplication, and division.

Complex Numbers: Operations and Applications Log in to Mediaspace to watch this video

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

Complex Numbers and 2x2 Matrices Log in to Mediaspace to watch this video

Covers complex numbers, quadratic equations, solutions in C, and 2x2 matrices.

Complex Numbers: Operations and Polar Form Log in to Mediaspace to watch this video

Explores complex numbers, operations, absolute value, and polar form, along with the analysis and graphic representation of complex numbers.