What is an Imaginary Number?

What is an Imaginary Number?

Note:

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.

Keywords:

  • imaginary number
  • numbers
  • square root
  • complex
  • i
  • definition
  • pure imaginary number

Background Tutorials

  • Write and evaluate numerical expressions involving whole-number exponents.

      • How Do You Square a Number?How Do You Square a Number?

      How Do You Square a Number?

      Want to square a number? Just take the number and multiply it by itself! If you square an integer, you get a perfect square! Check out squaring in this tutorial!

  • Know that numbers that are not rational are called irrational. Understand informally that every number has a decimal expansion; for rational numbers show that the decimal expansion repeats eventually, and convert a decimal expansion which repeats eventually into a rational number.

      • What's a Real Number?What's a Real Number?

      What's a Real Number?

      Real numbers are numbers that can be found on the number line. This includes both the rational and irrational numbers. This tutorial explains real numbers and gives some great examples. Take a look!

  • Know there is a complex number i such that i^2 = -1, and every complex number has the form a + bi with a and b real.

      • What is the Imaginary Unit i?What is the Imaginary Unit i?

      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.

  • Use the method of completing the square to transform any quadratic equation in x into an equation of the form (x - p)^2= q that has the same solutions. Derive the quadratic formula from this form.

      • What is a Quadratic Equation?What is a Quadratic Equation?

      What is a Quadratic Equation?

      You can't go through algebra without seeing quadratic equations. The graphs of quadratic equations are parabolas; they tend to look like a smile or a frown. There's also a bunch of ways to solve these equations! Watch this tutorial and get introduced to quadratic equations!

Further Exploration

  • Use the relation i^2 = -1 and the commutative, associative, and distributive properties to add, subtract, and multiply complex numbers.

      • How Do You Multiply Pure Imaginary Numbers?How Do You Multiply Pure Imaginary Numbers?

      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.