Table of Contents
 Permutations, Combinations, and the Binomial Theorem

Complex Numbers
 Polar Coordinates
 Argand Diagram
 Modulus of a Complex Number
 The Argument of a Complex Number
 Polar Form of Complex Numbers
 Operations on Complex Numbers in Polar Form
 Exponential Form of a Complex Number
 De Moivre’s Theorem
 De Moivre’s Theorem for Trigonometric Identities
 Cube Roots of Unity
 The 𝑛th Roots of Unity
 Arbitrary Roots of Complex Numbers
 Determinants and Matrices

Geometry and Measurement in Two and Three Dimensions
 Points, Midpoints, and Distances in Space
 Equation of a Sphere
 Vectors in Space
 Magnitude of a Vector in 3D
 Scalar Multiplication and Unit Vectors
 Direction Angles and Direction Cosines
 Vector Operations in 3D
 Dot Product in 2D
 Dot Product in 3D
 Angle between Two Vectors in Space
 Scalar Projection
 Cross Product in 2D
 Cross Product in 3D
 Parallel and Perpendicular Vectors in Space
 Scalar Triple Product

Straight Lines and Planes in Space
 Equation of a Straight Line in Space: Cartesian and Vector Forms
 Equation of a Straight Line in Space: Parametric Form
 Angle between Two Straight Lines in Space
 Parallel, Perpendicular, and Intersecting Lines in Space
 The Perpendicular Distance between Points and Straight Lines in Space
 Equation of a Plane: Vector, Scalar, and General Forms
 Equation of a Plane: Intercept and Parametric Forms
 The Angle between Two Planes and between a Plane and a Straight Line
 Equations of Parallel and Perpendicular Planes
 Intersection of Planes
 The Perpendicular Distance between Points and Planes