The natural numbers are used for counting.

By subtracting natural numbers from natural numbers, we can create whole numbers that are not natural numbers, such as the negative integers.

By dividing whole numbers by whole numbers we can create rational numbers that are not whole numbers, such as the fraction 1/2.

By taking the square roots of positive numbers we can create real numbers that are irrational.

Finally, by taking the square roots of negative numbers we create complex numbers that are imaginary (that is to say, not real).

The real numbers can be placed in a line that is sometimes called the real line.

The complex numbers can be placed in a plane that is known as the complex plane. This plane has two axes, the horizontal real axis on which the real numbers are placed, and the vertical imaginary axis on which the imaginary numbers are placed.

An imaginary number is a real number multiplied by the positive square root of -1. For this we use the symbol i:

i = √(-1).

Every complex number c is the sum of a real number a (the real part of c) and an imaginary number ib. Somewhat confusingly, the imaginary part of c is the real number b.

Do not be mislead by the whimsical tags "real" and "imaginary." No number is real in the sense in which, say, an apple is real. As creations of the human mind, the real numbers are no less imaginary (in the ordinary sense) than the so-called imaginary numbers. (Or if you believe that real numbers exist in their own Platonic world, then so do the imaginary numbers.) It's just that you don't need imaginary numbers for counting or measuring, which is why you may not be familiar with them.