# Ch 27: ACT Math: Complex Numbers

### About This Chapter

## ACT Math: Complex Numbers - Chapter Summary

Review the essential information about complex numbers for the algebra portion of the math test in the ACT. The topics below are included in the lessons:

- Imaginary numbers
- Adding, subtracting, multiplying and dividing complex numbers
- Solving quadratics with complex numbers as solutions

Our short, video lessons break down the steps of working with complex numbers into manageable pieces. As you work your way through the lessons, make sure that you complete the quick quizzes for self-assessment. Then you'll know of any areas needing more attention.

### ACT Math Objectives

You should understand the quadratic formula as a basis for the intermediate algebra portion of the ACT. Of the total 60 math questions on the exam, 15% of them test your understanding of these intermediate algebra topics:

- Quadratic formula
- Complex numbers
- Rational/radical expressions
- Absolute value equations/inequalities
- Sequences/patterns
- Systems of equations
- Functions
- Modeling
- Matrices
- Roots of polynomials
- Quadratic inequalities

You'll have 60 minutes to choose the correct answers for the 60 multiple-choice questions on the math exam. Our lessons and quizzes targeting these crucial topics will help you get ready for test day. You may choose to use an approved model of calculator, or complete your work with paper and pencil. Your ACT results will include a score for the entire test and sub-scores for combinations of algebra, geometry and trigonometry sections.

### 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 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.

### 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 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 ACT Prep: Practice & Study Guide course

- ACT: About the Test
- ACT English: Section Overview
- ACT English: Punctuation
- ACT English: Grammar and Usage
- ACT English: Sentence Structure
- ACT English: Parts of an Essay
- ACT English: Rhetorical Strategy
- ACT English: Organization
- ACT English: Style
- ACT Math: Overview
- ACT Math: Number & Quantity
- ACT Math: Pre-Algebra
- ACT Math: Algebraic Expressions
- ACT Math: Radicals
- ACT Math: Linear Equations
- ACT Math: Functions
- ACT Math: Types of Functions
- ACT Math: Absolute Value
- ACT Math: Matrices
- ACT Math: Inequalities
- ACT Math: Probability, Combinations & Factorial
- ACT Math: Data and Statistics
- ACT Math: Exponents
- ACT Math: Polynomials and Quadratics
- ACT Math: Rational Equations and Expressions
- ACT Math: Sequences
- ACT Math: Exponentials and Logarithms
- ACT Math: Coordinate Geometry
- ACT Math: Conic Sections
- ACT Math: Triangles
- ACT Math: Plane Geometry
- ACT Math: Lines and Angles
- ACT Math: Trigonometry
- ACT Science Reasoning: Overview
- ACT Science Reasoning: Fundamentals of Science
- ACT Science Reasoning: Evaluating Models
- ACT Reading: Overview
- ACT Reading: Question Types
- ACT Reading: Understanding Reading Passages
- ACT Reading: Word Meanings and Choice
- ACT Reading: Analyzing Reading Passages
- ACT Reading: Practice
- ACT Writing: Overview
- ACT Writing: Essay Skills
- ACT Writing: Planning and Writing
- ACT Writing: Advanced Writing Skills
- ACT Prep Flashcards