# Ch 13: High School Algebra: Complex and Imaginary Numbers

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### About This Chapter

## Complex and Imaginary Numbers - Chapter Summary and Learning Objectives

Imaginary numbers are represented by 'i' when calculating the square root of -1. Complex numbers occur when imaginary numbers are combined with real numbers. Our instructors have been tasked with showing you why imaginary and complex numbers are important as well how to perform basic operations with them. Our video lessons are provided with supplementary quizzes that can be used to judge your progress when learning about complex and imaginary numbers. After completing this chapter, you should be able to:

- Subtract, multiply and add complex numbers
- Graph complex numbers on a complex plane
- Divide complex numbers and conjugates
- Solve polynomials and quadratics with complex number solutions
- Explain what it takes for imaginary numbers to be transformed into real numbers.

Video | Objective |
---|---|

What is an Imaginary Number? | Define what imaginary and complex numbers are. Also, explain their importance. |

How to Add, Subtract and Multiply Complex Numbers | Learn how to subtract, multiply and add complex numbers. |

How to Divide Complex Numbers | Describe how to divide complex numbers and conjugates. |

How to Graph a Complex Number on the Complex Plane | Demonstrate graphing complex numbers on a complex plane. |

How to Solve Quadratics with Complex Numbers as the Solution | Explain how to solve quadratics and polynomials that have solutions featuring complex numbers. |

### 1. What is an Imaginary Number?

The imaginary number 'i' is the square root of -1. Although this number doesn't actually exist, pretending that it does allows us to do a bunch of crazy math that scientists use every day. Learn the basics of that number 'i' here!

### 2. How to Add, Subtract and Multiply Complex Numbers

Knowing that complex numbers exist is the first step. But that knowledge alone won't help you do much with them. Learn the basics of complex number addition, subtraction and multiplication here!

### 3. How to Divide Complex Numbers

While adding, subtracting and multiplying complex numbers is pretty straightforward, dividing them can be pretty tricky. It comes down to the process of multiplying by the complex conjugate. Learn about what that is, and how to do it, here.

### 4. How to Graph a Complex Number on the Complex Plane

Graphing complex numbers is pretty straight forward, but it's not necessarily intuitive. Check out this lesson to learn the vocabulary and the conventions that you'll need.

### 5. How to Solve Quadratics with Complex Numbers as the Solution

When you solve a quadratic equation with the quadratic formula and get a negative on the inside of the square root, what do you do? The short answer is that you use an imaginary number. For the longer, more helpful answer, check out this lesson!

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### Other Chapters

Other chapters within the Remedial Algebra I course

- High School Algebra: Basic Arithmetic
- High School Algebra: Solving Math Word Problems
- High School Algebra: Decimals and Fractions
- High School Algebra: Percent Notation
- High School Algebra: Real Numbers
- High School Algebra: Exponents and Exponential Expressions
- High School Algebra: Radical Expressions
- High School Algebra: Algebraic Expressions and Equations
- High School Algebra: Properties of Functions
- High School Algebra: Matrices and Absolute Value
- High School Algebra: Working With Inequalities
- High School Algebra: Properties of Exponents
- High School Algebra: Algebraic Distribution
- High School Algebra: Linear Equations
- High School Algebra: Factoring
- High School Algebra: Graphing and Factoring Quadratic Equations
- High School Algebra: Properties of Polynomial Functions
- High School Algebra: Rational Expressions
- High School Algebra: Cubic Equations
- High School Algebra: Quadratic Equations
- High School Algebra: Measurement and Geometry
- High School Algebra: Calculations, Ratios, Percent & Proportions
- High School Algebra: Data, Statistics, and Probability
- High School Algebra: Well-Known Equations