Elementary Properties of Complex Numbers

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Complex Numbers: Introduction and Properties

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

Gauss Representation

Explores the Gauss representation of complex numbers, focusing on addition, multiplication, bases, and vector space dimensions.

Complex Numbers: Polar Form

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

Absolute Value and Complex Numbers

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

Complex Exponential: Properties and Formulas

Delves into complex exponential functions, their properties, and polar representation of complex numbers.

Polynomials: Operations and Properties

Explores polynomial operations, properties, and subspaces in vector spaces.

Module Theory: Definitions and Examples

Introduces the definition and examples of A-modules, including sub-modules and ideals.

Complex Numbers: Polar Representation

Explores the polar representation of complex numbers and its applications.

Linear Equations and Matrices: Solution Methods, Elementary Operations

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

Magnetic Fields and Complex Numbers

Explores magnetic fields from moving charges and the properties of complex numbers.