Complex numbers, also known as imaginary numbers, began as a way to find the square roots of negative numbers. No real number (-1, 0, 1, 2, pi, 4.7, 2000, etc.) squared will give a negative answer. A new set of numbers had to be invented. The square root of negative 1 was defined as i. The square root of -4 can be shown to be 2 times the square root of -1, or 2i.

What happens when a real number is added to an imaginary number? For example, what is 1 + i? The answer is 1 + i. Complex numbers have two parts -- the real part and the imaginary part. When adding complex numbers, each part is added normally to the corresponding part of the other number. For example, (2 + 3i) + (4 + 5i) = (6 + 8i). It is also possible to multiply, divide, and find roots of complex numbers, although the rules get a little more complicated.

Any real number can be located on a number line. To plot complex numbers, the complex plane had to be invented. The real part of a complex number corresponds to the x coordinate, and the imaginary part corresponds to the y coordinate. On the complex plane, 1 is 1 unit to the right of the origin (0), i is one unit above the origin, 1+2i is 2 units above and 1 unit to the right of the origin.