Chapter 1: Number Systems

Welcome to the first chapter of your mathematics journey. This introductory lesson will give you a roadmap of what you'll learn, explore, prove, and practice in the topic of Number Systems. This chapter sets the foundation that underlies advanced topics.

What You'll Learn

We'll explore different types of numbers and their properties, including:

• Types of Numbers:
  • Natural Numbers
  • Whole Numbers
  • Integers
  • Rational Numbers
  • Irrational Numbers
  • Real Numbers
  • Transcendental Numbers
  • Complex Numbers
• Types of Decimals:
  • Terminating and Non-Terminating Decimals
  • Recurring and Non-Recurring Decimals
• Properties:
  • Properties of Real Numbers
  • Properties of Equality
  • Properties of Inequality
  • Properties of Complex Numbers
• Complex Number Topics:
  • Argand Diagram
  • Simplifying Powers of Iota
  • Factorization using Complex Numbers
  • de-Moivre's Theorem

Proofs You Will Explore

• $\sqrt{2}$ is irrational
• $\sqrt{3}$ is irrational
• $\sqrt{5}$ is irrational
• Sum of like and unlike fractions
• Properties of modulus and conjugates of complex numbers
• Proof of de-Moivre's Theorem

Visual Representations

You'll be presented with visual explanations and interactive illustrations of:

• The Number Line
• The Coordinate Plane
• The Complex Plane (Argand Diagram)
• Operations on Complex Numbers:
  • Addition
  • Multiplication
  • Division
  • Conjugation

Interactive Activities & Exercises

Practice your understanding through engaging activities such as:

• Matching & Drag-and-Drop:
  • Match number sets with their definitions
  • Build properties of real numbers
  • Build properties of equality and inequality
• True/False Challenges:
  • Test your understanding of real number properties
• Dynamically Generated Questions:
  • Addition, multiplication, and division of complex numbers
  • Finding the multiplicative inverse of complex numbers
  • Converting negative square roots into iota form
  • Simplifying powers of iota $i$
  • Simplifying complex numbers using de-Moivre’s Theorem
  • Identifying properties used in mathematical statements
  • Finding the polar forms of complex numbers
• Algebra with Complex Numbers:
  • Factorization of algebraic expressions using complex numbers

Get Ready to Begin

This chapter sets the tone for everything that follows. Each lesson builds upon these core ideas. Whether you're matching terms, dragging equations into place, or solving interactive proofs, everything you learn here is essential groundwork for algebra, calculus, and beyond.

Click on the modules button on bottom left to open the navigation. Or click Next to start your first lesson.