What is the Imaginary Unit i?

What is the Imaginary Unit i?

Note:

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.

Keywords:

  • imaginary unit
  • i
  • imaginary numbers
  • complex
  • square root of a negative
  • definition

Background Tutorials

  • Evaluate expressions at specific values of their variables. Include expressions that arise from formulas used in real-world problems. Perform arithmetic operations, including those involving whole-number exponents, in the conventional order when there are no parentheses to specify a particular order (Order of Operations).

      • What is a Variable?What is a Variable?

      What is a Variable?

      You can't do algebra without working with variables, but variables can be confusing. If you've ever wondered what variables are, then this tutorial is for you!

  • Know and apply the properties of integer exponents to generate equivalent numerical expressions.

      • What are Exponents?What are Exponents?

      What are Exponents?

      Did you know that another word for 'exponent' is 'power'? To learn the meaning of these words and to see some special cases involving exponents, check out this tutorial!

  • 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 an Imaginary Number?What is an Imaginary Number?

      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.

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

      • How Do You Simplify the Square Root of a Negative Number?How Do You Simplify the Square Root of a Negative Number?

      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.

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.