What are complex and imaginary numbers and how are they different from normal (real) numbers?

When you think of a number line, zero lies at the centre and the positive numbers stretch off to the right, while negative numbers go off left. This is a representation of real numbers, including both rational (e.g. 3/7) and irrational (e.g. pi or root 2). There also exists a class of numbers called imaginary numbers. Imaginary numbers contain the imaginary unit, i, as a factor, where i is the square root of -1. i was considered until relatively recently to not exist, but is often found as, for example, the solution to polynomial equations. Going back to the number line, we will convert the real number line into the x axis on a plane. The new y axis represents imaginary numbers, with positive multiples of i going up, and negative going down. This plane, called the complex plane, represents both real and imaginary numbers, and includes complex numbers which contain both real and imaginary parts and may lie off either axis. Examples of numbers on the complex plane: Real: 3, 6/11, pi Imaginary: i, -4i, 8.26i Complex: 2.3 + 3i, 3, 8i (either the real or imaginary part of a complex number may be 0)