# Ch 5: Saxon Algebra 2: Complex Numbers

### About This Chapter

## How It Works:

- Identify the lessons in the Saxon Complex Numbers chapter with which you need help.
- Find the corresponding video lessons with this companion course chapter.
- Watch fun videos that cover the complex numbers topics you need to learn or review.
- Complete the quizzes to test your understanding.
- If you need additional help, rewatch the videos until you've mastered the material or submit a question for one of our instructors.

## Students will learn:

- Imaginary numbers
- Standard form for complex numbers
- Arithmetic using complex numbers
- Finding complex roots
- Examples of complex conjugates

*Saxon is a registered trademark of Houghton Mifflin Harcourt, which is not affiliated with Study.com.*

### 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. Using the Standard Form for Complex Numbers

Complex numbers are numbers that have two components. One component is the real part, and the other one is the imaginary part. The standard form of a complex number is ''a'' + ''b''i, where ''a'' is real and ''b''i is imaginary. This lesson will cover the standard form and provide examples.

### 3. 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!

### 4. 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.

### 5. Complex Conjugate: Numbers, Functions & Examples

After completing this lesson, you will be able to describe and define complex conjugates. You will also be able to write complex conjugates and use them appropriately to solve problems.

### 6. Finding Complex Roots of Quadratic Equations

In this lesson, we will see how to find complex roots of quadratic equations using the quadratic formula. We will also look at what the graph of a quadratic equation with complex roots looks like.

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### Other Chapters

Other chapters within the Saxon Algebra 2 Homeschool: Online Textbook Help course

- Saxon Algebra 2: Decimal Numbers
- Saxon Algebra 2: Graphs on the Coordinate Plane
- Saxon Algebra 2: Sets
- Saxon Algebra 2: Real Numbers
- Saxon Algebra 2: Conversion by Unit Multipliers
- Saxon Algebra 2: Ratio & Proportion
- Saxon Algebra 2: Percent
- Saxon Algebra 2: Rate
- Saxon Algebra 2: Exponents
- Saxon Algebra 2: Exponents on a Scientific Calculator
- Saxon Algebra 2: Roots
- Saxon Algebra 2: Probability
- Saxon Algebra 2: Statistics
- Saxon Algebra 2: Simplifying Expressions
- Saxon Algebra 2: Polynomials
- Saxon Algebra 2: Simplifying Rational Expressions
- Saxon Algebra 2: Simplifying and Solving Equations
- Saxon Algebra 2: Linear Equations
- Saxon Algebra 2: Solving Linear Equations
- Saxon Algebra 2: Quadratic Equations
- Saxon Algebra 2: Other Types of Equations
- Saxon Algebra 2: Understanding Functions
- Saxon Algebra 2: Manipulating and Evaluating Functions
- Saxon Algebra 2: Trigonometry
- Saxon Algebra 2: Logarithms
- Saxon Algebra 2: Lines, Points, Segments, and Planes
- Saxon Algebra 2: Angles
- Saxon Algebra 2: Polygons
- Saxon Algebra 2: Circles
- Saxon Algebra 2: Triangles
- Saxon Algebra 2: Geometric Solids
- Saxon Algebra 2: Perimeter and Circumference
- Saxon Algebra 2: Area
- Saxon Algebra 2: Surface Area and Volume
- Saxon Algebra 2: Constructions
- Saxon Algebra 2: Postulates & Pythagorean Theorem
- Saxon Algebra 2: Proofs