Ch 23: Imaginary & Complex Numbers

About This Chapter

Refresh your knowledge of complex and imaginary numbers with this chapter. These lessons and quizzes can be used as a comprehensive study guide to help you prepare for an upcoming test or placement exam.

Imaginary & Complex Numbers - Chapter Summary

This chapter will define imaginary and complex numbers and explain how to add, subtract, divide and multiply complex numbers. You will also learn to graph a complex number on the complex plane.

Your study will continue with a review of how to solve quadratic equations that contain complex numbers as the solution and how to write complex numbers in polar form. This chapter will help you understand how to:

  • Explain what an imaginary number is
  • Add, subtract and multiply complex numbers
  • Graph complex numbers
  • Solve quadratic equations involving complex numbers
  • Use De Moivre's Theorem

Use our chapter tests and lesson quizzes to gauge how well you understand the material and where you might need to study further. These materials have been designed by knowledgeable instructors who want to make sure that you successfully learn the above topics. As you read through the chapter, contact one of our instructors if you require assistance.

5 Lessons in Chapter 23: Imaginary & Complex Numbers
Test your knowledge with a 30-question chapter practice test
What is an Imaginary Number?

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!

How to Add, Subtract and Multiply Complex Numbers

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!

How to Divide Complex Numbers

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.

How to Graph a Complex Number on the Complex Plane

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.

How to Solve Quadratics with Complex Numbers as the Solution

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!

Chapter Practice Exam
Test your knowledge of this chapter with a 30 question practice chapter exam.
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Practice Final Exam
Test your knowledge of the entire course with a 50 question practice final exam.
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Other Chapters

Other chapters within the MTLE Middle Level Mathematics: Practice & Study Guide course