Lectures related to Complex Numbers: Argument and Polar Method

Complex Numbers: Polar Form

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

Complex Roots: Conjugate Pairs and Quadratic Equations

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

Complex Numbers: Polar Form

Explains the polar form of complex numbers and Euler's formula in the complex plane.

Complex Numbers: Polar Form

Covers the polar form of complex numbers, emphasizing the importance of the argument.

Complex Roots and Polynomials

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

Absolute Value and Complex Numbers

Covers the absolute value function, complex numbers, Euler's formula, and trigonometry applications.

Complex Numbers and 2x2 Matrices

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

Characteristic Polynomials and Similar Matrices

Explores characteristic polynomials, similarity of matrices, and eigenvalues in linear transformations.

Complex Numbers: Operations and Properties

Explores complex numbers, including modulus, conjugation, and Euler formula.

Complex Numbers: Introduction and Operations

Introduces complex numbers and their forms, including Cartesian, polar, and exponential forms, and explains how to find the argument of a complex number.

Polynomials with Real Coefficients

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

Circular Trigonometry: Understanding Geometric Angles

Explores the concept of angles in circular trigonometry, emphasizing geometric angles and their properties.

Sequences: Definitions and Examples

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

Square Roots and Complex Numbers

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

Integration of Rational Functions

Covers the integration of rational functions and the decomposition into irreducible factors.

Complex Numbers: Properties and Operations

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

Complex Numbers: Operations and Applications

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

The Fundamental Theorem of Algebra

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

Complex Numbers: Polar Representation

Explores the polar representation of complex numbers and its applications.

Complex Numbers: Polar Form

Explores complex numbers in polar form, Euler's formula, and coordinate transformation.