The Complex Number System

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What are the Commutative Properties of Addition and Multiplication?

The commutative property is a fundamental building block of math, but it only works for addition and multiplication. This tutorial defines the commutative property and provides examples of how to use it.
What is the Distributive Property?

The distributive property is a very deep math principle that helps make math work. It's the rule that lets you expand parentheses, and so it's really critical to understand if you want to get good at simplifying expressions. So check out the tutorial and let us know what you think!
What are the Associative Properties of Addition and Multiplication?

The associative property is one of those fundamental properties of math that make math work. You probably take this property for granted because it's so ingrained, but it's important to see how the guts of math work, so check out the tutorial and make sure you're solid on your fundamentals!
How Do You Multiply Pure Imaginary Numbers?

You can multiply imaginary numbers like you multiply variables. Just remember that 'i' isn't a variable, it's an imaginary unit! This tutorial shows you the steps to find the product of pure imaginary numbers.
How Do You Multiply Complex Numbers Using FOIL?

Get some practice multiplying complex numbers together using the FOIL method! This tutorial takes you through the process of multiplying two complex numbers together.
How Do You Add Complex Numbers?

If you want to add complex numbers together, first regroup them so that like terms are next to one another. Then, add the like terms together, and you have your answer! To see an example, check out this tutorial.
How Do You Subtract Complex Numbers?

When you subtract complex numbers, you first need to distribute in the minus sign into the second complex number. Then, regroup the terms so like terms are next to each other. Combine those like terms, and you have the answer! Watch this tutorial to see a great example!
How Do You Find the Absolute Value of a Complex Number?

The absolute value of a complex number is just the distance from the origin to that number in the complex plane! This tutorial shows you how to use a formula to find the absolute value of a complex number.
How Do You Graph Complex Numbers?

To understand a complex number, it's important to understand where that number is located on the complex plane. This tutorial helps you practice graphing complex numbers!
How Do You Divide Complex Numbers Using Conjugates?

To divide complex numbers, you usually need to multiply by the complex conjugate of the denominator. Follow along with this tutorial to see how to find that complex conjugate and multiply with it to perform the division!
How Do You Find Higher Powers of i?

When the imaginary number 'i' has a large exponent, it can take a while to simplify it. Luckily, this tutorial gives you a trick to quickly find a higher power of 'i'!
How Do You Simplify the Square Root of a Negative Number?

Simplifying the square root of a negative number is very similar to simplifying the square root of a positive number. You just need to remember 'i' in your answer! Check out this tutorial to see how to simplify the square root of a negative number.
How Do You Add Complex Numbers by Graphing in the Complex Plane?

Did you know you can add two complex numbers together just by graphing them? This tutorial shows you how you can perform this addition on the complex plane!
How Do You Use the Square Root Method to Solve a Quadratic Equation with Imaginary Solutions if a≠1?

The solution to a quadratic equation can sometimes be an imaginary number! This tutorial shows you how to use the square root method to solve a quadratic equation that has imaginary solutions.
How Do You Solve a Quadratic Equation With Complex Solutions by Using the Quadratic Formula?

You can never get too much practice working with the quadratic formula, especially when the solution includes complex numbers! Watch this tutorial to see the quadratic formula be used to find the complex solutions to a quadratic equation.
How Do You Use the Square Root Method to Solve a Quadratic Equation with Imaginary Solutions?

There are many ways to solve a quadratic equation. One of these ways is by using the square root method. Watch this tutorial to see how the square root method is used to solve a quadratic equation and find imaginary solutions!
How Do You Solve a Quadratic Equation with Complex Solutions by Completing the Square?

You can solve a quadratic equation by completing the square! This tutorial shows you the steps needed to solve a quadratic using this method.
How Do You Find Values for x and y to Make Two Complex Numbers Equal?

Solving complex numbers isn't as complex as you might think. Just match up the real parts and the imaginary parts and solve! This tutorial shows you how to solve an equation involving complex numbers for specific variables.
What is the Imaginary Unit i?

Every tried to take the square root of a negative number? You'll need the imaginary unit 'i' to write the answer. This tutorial introduces you to this useful imaginary unit.
What is an Imaginary Number?

Imaginary numbers are used to help us work with numbers that involve taking the square root of a negative number. In this tutorial, you'll be introduced to imaginary numbers and learn that they're a type of complex number.
What is the Fundamental Theorem of Algebra?

Does every polynomial function have a solution? The answer can be found through the Fundamental Theorem of Algebra! This tutorial introduces you to the theorem and explains how its meaning.