# Ch 2: Algebra Concepts

### About This Chapter

## Algebra Concepts - Chapter Summary

Our instructors will explain the properties and definition of a real number and what exactly the binary number system is. You'll be introduced to other number systems and the algebraic concepts of groups and sets. How to use relation in mathematics is also covered.

Your study continues with instructions on how to find the cartesian product, as well as an explanation of what a complex number is and what the modulus of a complex number consists of. After you review these lessons, you should be able to:

- Give examples of real numbers
- Compare decimals using the number line
- Understand the basic rules of arithmetic
- Detail the base-ten system
- Use Venn diagrams
- Combine complex numbers using addition and subtraction
- Define the modulus of a complex number
- Apply imaginary cube roots of unity

Access these mobile-friendly lessons and quizzes at any time, seven days a week. Each lesson is accompanied by a printable transcript so you can review the material offline any time. As you read through the chapter, contact one of our instructors if you need more help.

### 1. What are Real Numbers? - Definition & Properties

There are many definitions of real numbers, but they all lead to the same conclusion. Real numbers are numbers that have a measurable value. Learn more about real numbers with some examples and a quiz to test your knowledge.

### 2. Using the Number Line to Compare Decimals, Fractions, and Whole Numbers

Watch this video lesson to learn how useful the number line can be when you need to compare two different numbers, be they whole numbers, decimals or even fractions. Learn how to plot these numbers on the number line so you can compare them.

### 3. Basic Arithmetic: Rules & Concepts

This lesson provides basic rules and concepts of arithmetic, the area of math that involves addition, subtraction, multiplication, and division. This lesson shares details about each operation and how they relate to one another in arithmetic.

### 4. What is the Binary Number System? - Definition & History

If you have spent any time around computers, you have probably heard of the binary number system. But what is it, exactly, and why is it so essential to modern computing? In this lesson we'll explore this fascinating topic.

### 5. Number Systems and The Base-Ten System

Ever think that a computer doesn't get what you want it to do? Don't be surprised; it is living in a world where it can only count to 1. This lesson explains number systems, including our base-ten system and a computer's base-two system.

### 6. Introduction to Groups and Sets in Algebra

As an introduction to the algebraic concepts of sets and groups, this lesson covers the difference between the two concepts and how to determine if a set is a group. To complete this lesson, we'll take a look at some practice examples.

### 7. Venn Diagrams: Subset, Disjoint, Overlap, Intersection & Union

The Venn diagram was introduced by John Venn. Yes, the Venn diagram is named after a real person! His idea was to show sets in terms of pictures. The Venn diagram is now used in many fields, including mathematics. Let's take a look at John Venn's idea.

### 8. Relation in Math: Definition & Examples

In this lesson, you will learn the definition of relation in terms of mathematics, as well as the various ways of displaying relations. We will also look at some examples.

### 9. How to Find the Cartesian Product

The Cartesian product allows us to take two sets of mathematical objects and create one new one. With one simple idea, the Cartesian product becomes quick and easy.

### 10. What is a Complex Number? - Definition & Properties

Applications of complex numbers include signal processing filters in engineering and vector length calculations in physics. After defining complex numbers, this lesson explores how to combine them using addition, subtraction and multiplication.

### 11. Modulus of a Complex Number: Definition & Examples

In this lesson, we will explore complex numbers and an important characteristic of these numbers called a modulus. We will look at what a modulus of a complex number is, how it relates to other aspects of a complex number, and how to find it.

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### Other Chapters

Other chapters within the NDA Exam Preparation & Study Guide course

- About the NDA Exam
- Advanced Algebra Concepts
- Solving Matrices & Determinants
- Trigonometry Concepts
- Geometry & Linear Equations
- Analytic Geometry
- Functions, Limits & Continuity
- Derivative Rules
- Calculations & Applications of Derivatives
- Integral Calculus
- Differential Equations & Applications
- Scalars & Vectors in Algebra
- Visualizing Statistics
- Probability Concepts in Math
- Grammar and Usage
- Improving Reading Comprehension
- Measurements in Physics
- Motion in Physics
- Basics of Work, Power & Energy
- Understanding Heat Transfer
- Sound Waves
- Light, Mirrors & Lenses
- Magnets
- Electric Currents & Power
- Scientific Technology, Machines & Tools
- The Atom & Structure of Elements
- Chemical Properties of Elements & Substances
- Chemical Symbols, Formulas & Reactions
- Qualities of Living Organisms
- Health Science Basics
- Solar System & Eclipses
- Achievements of Famous Scientists
- Indian History
- Overview of Major World History Events
- World Government Types
- The Earth
- Earth's Oceans, Atmosphere & Climate
- Regional Geography of South Asia
- Modern Day Events in India
- NDA Exam Preparation & Study Guide Flashcards