Lectures related to Complex Logarithm: Extension and Polar Form

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

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

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

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

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

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

Explores complex hyperbolic and trigonometric functions, defining key properties and relationships with exponential functions.

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

Covers the introduction and operations of complex numbers in physics and engineering applications.

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

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

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

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

Covers the definitions and properties of complex numbers, including conjugate and modulus.

Covers complex numbers, derivatives, and solutions of the damped harmonic oscillator with different damping regimes.

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

Explores complex numbers, roots, equations, and polynomial factorization with real coefficients.

Explores holomorphic functions, Cauchy-Riemann conditions, and principal argument values in complex analysis.

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

Covers examples related to complex numbers and their properties.