Lectures related to Complex Numbers: Roots and Equations

Complex Numbers: Polar Form

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

Complex Numbers: Operations and Applications

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

Complex Numbers: Operations, Polar Form, and Solutions

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

Complex Numbers: Properties and Operations

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

Complex Roots and Polynomials

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

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.

Absolute Value and Complex Numbers

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

Complex Numbers: Exponential Formulas

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

Complex Numbers: Representation and Properties

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

Complex Numbers: Operations and Properties

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

Complex Numbers: Representations and Rotations

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

Harmonic Forms: Main Theorem

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

Examples: Polynomial Factorization

Covers polynomial factorization examples and polynomial division in complex numbers.

Complex Numbers: Definitions and Applications

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

Complex Numbers: Trigonometric Formulas

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

Complex Numbers: Polar Form

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

Euler's Formula Demonstration

Covers the demonstration of Euler's formula and its applications.

Complex Numbers: Roots and Polynomials

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

Complex Numbers: Polar Form

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