The set of real numbers is closed under addition, subtraction, multiplication, and division. There is sometimes more than one way to write a decimal number. For example, 1.0 and 0.99999 are the same number. There are irrational numbers which have decimals that are infinite and non repeating but cannot be written as roots. In other words, what number when multiplied by itself gives 4.
Every positive number has two square roots.
Every time you square a number you end up with a positive number. If such a solution is desired, new numbers must be invented. In fact it is no more imaginary than any other number but the name has stuck. Let us have a look at some of the properties of this strange number. It is possible to have a combination of real and imaginary numbers.