# Ch 15: Complex Numbers in Math: Tutoring Solution

### About This Chapter

## How it works:

- Begin your assignment or other SAT math work.
- Identify the complex numbers concepts that you're stuck on.
- Find fun videos on the topics you need to understand.
- Press play, watch and learn!
- Complete the quizzes to test your understanding.
- As needed, submit a question to one of our instructors for personalized support.

## Who's it for?

This chapter of our SAT Mathematics Level 2 Tutoring Solution will benefit any student who is trying to learn about complex numbers to prepare for the subject test. This resource can help students, including those who:

- Struggle with understanding imaginary numbers, arithmetic operations with complex numbers, the complex plane or any other complex numbers topic
- Have limited time for studying
- Want a cost effective way to supplement their math learning
- Prefer learning math visually
- Find themselves failing or close to failing their complex numbers unit
- Cope with ADD or ADHD
- Want to excel on the SAT mathematics level 2 subject test
- Don't have access to their math teacher outside of class

## Why it works:

**Engaging Tutors**: We make learning about complex numbers simple and fun.**Cost Efficient**: For less than 20% of the cost of a private tutor, you'll have unlimited access 24/7.**Consistent High Quality**: Unlike a live math tutor, these video lessons are thoroughly reviewed.**Convenient**: Imagine a tutor as portable as your laptop, tablet or smartphone. Learn about complex numbers on the go!**Learn at Your Pace**: You can pause and re-watch lessons as often as you'd like, until you master the material.

## Learning Objectives

- Review the process for solving quadratics with complex numbers as the solution.
- Learn how to graph a complex number on the complex plane.
- Perform operations, such as adding, subtracting and multiplying, with complex numbers.
- Practice dividing complex numbers.
- Define imaginary numbers.

### 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.

### 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!

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### Other Chapters

Other chapters within the SAT Subject Test Mathematics Level 2: Tutoring Solution course

- SAT Math Level 2 Structure & Strategy: Tutoring Solution
- Basic Math Review: Tutoring Solution
- Square Roots: Tutoring Solution
- Basic Algebraic Expressions in Math: Tutoring Solution
- Exponents in Math: Tutoring Solution
- Vectors: Tutoring Solution
- Linear Equations & Inequalities in Algebra: Tutoring Solution
- Absolute Value Equations & Inequalities: Tutoring Solution
- Polynomials in Algebra: Tutoring Solution
- Functions in Math: Tutoring Solution
- Rational Expressions in Algebra: Tutoring Solution
- Matrices: Tutoring Solution
- Sequences and Series in Math: Tutoring Solution
- Exponentials and Logarithms in Math: Tutoring Solution
- Coordinate Geometry Basics: Tutoring Solution
- Graphing Linear Equations & Inequalities: Tutoring Solution
- Advanced Coordinate Geometry: Tutoring Solution
- Three-Dimensional Geometry: Tutoring Solution
- Overview of Trigonometry: Tutoring Solution
- Probability, Combinations & Permutations: Tutoring Solution
- Working with Data & Statistics: Tutoring Solution
- Logic: Tutoring Solution
- Limits in Math: Tutoring Solution