Lectures related to Complex Numbers: Definitions and Properties

Complex exponentials: Oscillations and advantages

Explores the use of complex exponentials to simplify trigonometry and algebra in digital systems.

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

Complex Numbers: Definitions and Properties

Covers the definitions and properties of complex numbers, including the field of complex numbers, the conjugate, the real and imaginary parts, algebraic form, modulus, and argument.

Complex Numbers: Definition

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

Absolute Value and Complex Numbers

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

Complex Numbers: Properties and Operations

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

Examples: Complex Numbers

Covers examples related to complex numbers and their properties.

Complex Numbers: Imaginary Part

Demonstrates how to determine the imaginary part of a complex number.

Complex Numbers: Roots and Polynomials

Covers the properties of complex numbers, including finding roots and factorizing polynomials.

Complex Numbers: Representations and Rotations

Explores the representation and rotation of complex numbers in the complex plane.

Complex Logarithm: Extension and Polar Form

Covers the extension of the logarithm to complex numbers and explores the relationship with trigonometric functions.

Complex Numbers: Exponential Formulas

Covers the activation process of a home connection and explores exponential formulas, Euler's formula, and complex equations.

Complex Numbers: Notations and Operations

Covers notations, operations, isomorphism, and polar decomposition of complex numbers.

Fundamental Theorem of Algebra

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

Complex Numbers: Polar Form

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

Complex Numbers: Representation and Properties

Covers the representation of complex numbers and their properties, including Euler's and Moivre's formulas.

Complex Numbers: Definitions and Applications

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

Complex Numbers: Polar Form, Powers, Roots

Explores complex numbers in polar form, powers, and roots, including trigonometric relationships and rotation matrices.

Harmonic Forms: Main Theorem

Explores harmonic forms on Riemann surfaces and the uniqueness of solutions to harmonic equations.

Complex Numbers: Trigonometric Formulas

Explores complex numbers, trigonometric functions, De Moivre's formulas, and complex plane representation.