# Ch 2: Algebra II: Complex and Imaginary Numbers Review

### About This Chapter

## Algebra II: Complex and Imaginary Numbers Review - Chapter Summary and Learning Objectives

The idea of working with numbers that don't really exist might sound confusing, but our experienced instructors have come up with several examples and sample problems to make concepts like negative square roots, complex numbers and imaginary axes believable enough. By the time you've finished viewing the lessons and quizzes included in this chapter, you should be able to do the following:

- Add, subtract, multiply and divide complex numbers
- Describe the differences between a coordinate and complex plane
- Solve polynomial equations with complex solutions

Video | Objectives |
---|---|

What is an Imaginary Number? | Learn why we use imaginary numbers to represent the square root of a negative number. Find out how they form complex numbers when combined with a real number. |

How to Add, Subtract and Multiply Complex Numbers | Follow steps for combining like terms and using the distributive property to add, subtract and multiply complex numbers. |

How to Divide Complex Numbers | Observe how a complex number's conjugate can be used to divide complex numbers. |

How to Graph a Complex Number on the Complex Plane | Learn how complex numbers are graphed on a real and imaginary axis. |

How to Solve Quadratics with Complex Numbers as the Solution | Use the discriminant to determine whether or not a quadratic equation has complex solutions. Explore uses of the zero product property to multiply higher order polynomials with complex solutions. |

### 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 Algebra II: High School course

- Algebra II: Real Numbers
- Algebra II: Exponents and Exponential Expressions Review
- Algebra II: Properties of Functions Review
- Algebra II: Linear Equations Review
- Algebra II: Systems of Linear Equations
- Algebra II: Inequalities Review
- Algebra II: Absolute Value Review
- Algebra II: Graphing and Factoring Quadratic Equations Review
- Algebra II: Quadratic Equations
- Algebra II: Factoring
- Algebra II: Polynomials
- Algebra II: Rational Expressions
- Algebra II: Graphing and Functions
- Algebra II: Conic Sections
- Algebra II: Roots and Radical Expressions Review
- Algebra II: Exponential and Logarithmic Functions
- Algebra II: Sequences & Series
- Algebra II: Combinatorics
- Algebra II: Calculations, Ratios, Percent & Proportions Review
- Algebra II: Statistics
- Algebra II: Trigonometry
- Homeschool Resources for High School Algebra II