About This Chapter
Working with Complex Numbers - Chapter Summary and Learning Objectives
Use the lessons included here to wrap your head around the idea of imaginary numbers and explore their place alongside real numbers on the complex plane. Our instructors provide you with a simple explanation of how imaginary numbers make it possible to work with expressions that include negative square roots - which technically don't exist - and show you the steps involved in solving equations with these types of numbers. Take advantage of the short instructional videos, their matching transcripts and the multiple-choice quizzes included here to learn how to do the following:
- Define an imaginary number
- Perform arithmetic operations with complex numbers
- Find the complex conjugate of a binomial
- Graph complex numbers on the complex plane
|What Is an Imaginary Number?||Learn how imaginary numbers are used to represent the square root of a negative number. Find out what makes up a complex number.|
|How to Add, Subtract and Multiply Complex Numbers||Apply formulas for adding and subtracting complex numbers. Study the order of operations used to multiply complex numbers.|
|How to Divide Complex Numbers||Understand how to find a binomial's complex conjugate. Learn how it can be used to divide complex numbers.|
|How to Graph a Complex Number on the Complex Plane||Practice graphing complex numbers on the complex plane's real and imaginary axes.|
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.
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Other chapters within the Precalculus: High School course
- Working With Inequalities
- Absolute Value Equations
- Introduction to Quadratics
- Working with Quadratic Functions
- Basics of Polynomial Functions
- Working with Higher-Degree Polynomials
- Graphing Piecewise Functions
- Understanding Function Operations
- Graph Symmetry
- Graphing with Functions
- Rate of Change
- Rational Functions & Difference Quotients
- Rational Expressions and Function Graphs
- Exponential Functions & Logarithmic Functions
- Using Trigonometric Functions
- Trigonometric Graphs
- Trigonometric Applications
- Solving Trigonometric Identities
- Vectors, Matrices and Determinants
- Mathematical Sequences and Series
- Sets in Algebra
- Analytic Geometry and Conic Sections
- Polar Coordinates and Parameterizations