About This Chapter
Solving & Graphing Complex Numbers - Chapter Summary
If you need to practice solving and graphing complex numbers, this college algebra chapter can help you do just that. This collection of simple and straightforward lessons outline imaginary numbers, complex equations, complex planes and more. You'll also walk through the steps needed to add, subtract, multiply and divide complex numbers.
Interactive lesson quizzes are included to help you solidify your knowledge and practice these complex number concepts. Printable lesson transcripts are available to supplement your study and you can quickly find specific topics on your course Dashboard. This chapter is designed to help you:
- Understand key information about imaginary numbers
- Define and describe complex conjugates and use them to solve a variety of math problems
- Outline the rules for adding subtracting, multiplying and dividing complex numbers
- Graph complex numbers on a complex plane
- Explain the process of solving complex equations
- Use imaginary numbers to solve quadratics with complex numbers as the solution
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. 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.
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. 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.
6. Solving Complex Equations: Examples & Explanation
In this lesson, learn how to deal with the imaginary part of complex numbers. Learn how to multiply complex numbers together and how to solve complex equations that involve negative square roots.
7. 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 within the DSST Fundamentals of College Algebra: Study Guide & Test Prep course
- Operations with Basic Algebraic Expressions
- Polynomial Operations Overview
- Operations with Rational Expressions
- Exponential Expressions & Operations
- Using & Solving Linear Equations
- Matrices & Matrix Operations
- Absolute Value
- Graphing & Solving Inequalities
- Quadratic Equations & Inequalities
- Operations with Radicals
- Graphing, Analyzing & Writing Functions
- DSST Informational Resources
- DSST Fundamentals of College Algebra Flashcards