Single-Phase Sinusoidal Circuits: Complex Numbers

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Complex Numbers: Algebraic Structure

Explores the algebraic structure and properties of complex numbers, including Euler's and Moivre's formulas.

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 Analysis: Holomorphic Functions and Cauchy-Riemann Equations

Introduces complex analysis, focusing on holomorphic functions and the Cauchy-Riemann equations.

Complex Numbers: Representations and Rotations

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

Inverse Element for Multiplication

Covers the inverse element for multiplication and introduces the Euler and Moivre formulas in complex numbers.

Euler and Moivre Formulas

Covers Euler and Moivre formulas, addition formulas, properties of exponentials, and generalizing sine and cosine definitions to complex numbers.

Mechanics: Oscillator Harmonics

Explores harmonic oscillators' behavior under various damping conditions, covering Newton's laws, complex numbers, and Euler's formula.

Complex Numbers: Polar Representation

Explores the polar representation of complex numbers and its applications.