Complex Numbers

Multiplication and Division in Polar Form

Conjugate Complex Numbers and Properties of Modulus

De Moivre’s Theorem and Powers of Complex Numbers

Hyperbolic and Trigonometric Functions in the Complex Domain

Euler’s Formula and Exponential Form of Complex Numbers

Complex Polynomials and the Fundamental Theorem of Algebra

Geometric Representation and the Complex Plane

Applications of Complex Numbers in Geometry and Physics

Logarithms and Complex Powers

Complex Roots and Radicals of Complex Numbers

Roots of Unity and Their Geometric Properties

Algebraic Form of Complex Numbers and Basic Arithmetic Operations

Complex Equations and Loci in the Complex Plane

Polar Form, Modulus, and Argument of Complex Numbers

Complex Mappings and Transformations (Translations, Rotations, Scalings)