# What are imaginary numbers?

## Question:

What are imaginary numbers?

## Types of Numbers in Mathematics:

In mathematics, there are a lot of different types of numbers. Throughout the history of mathematics, there have been times when a certain type of number would come about that caused mathematicians to create a new type of number in order to be able to work with that number. Numbers such as this are often quite fascinating in the study of mathematics.

In mathematics, imaginary numbers are defined as numbers that contain the number i, where i is the number with value {eq}\sqrt{-1} {/eq}. These types of numbers are often square roots of negative numbers, and without the number i, it would be impossible to work with these types of numbers. Some examples of imaginary numbers are as follows:

• {eq}\sqrt{-7} {/eq} is an imaginary number, because it is the square root of a negative number, and we can write it as {eq}i\sqrt{7} {/eq}, so it contains the number i.
• 3 + 4i is an imaginary number, because it contains the number i.
• {eq}5-\sqrt{-4} {/eq} is an imaginary number, because it contains the square root of a negative, and it can be written as 5 - 2i, so it contains the number i.

We see that an imaginary number can be defined as any number that contains a square root of a negative number or the number i.