What is an imaginary number and how is it expressed?

An imaginary number is a number that cannot exist. An example of an imaginary number would be: the square root of negative nine, or any negative number.

When I try to think of any two of the same numbers that would multiply together to be negative nine, all I can think of is 3 or -3. when I square both of those numbers, I get the number 9, not -9. When I multiply two negatives together, I get a positive number, therefore there is no possible way to get the square root of -9, or any negative number.