An imaginary number is represented as ai where a is any positive or negative number, and i is a special constant whose square equals -1 (This means i*i = -1). While this constant may not exist in the normal number system, we may, for convenience, imagine it may, and we may then take the square root out of any negative number (sqrt(-4) == sqrt(4)*sqrt(-1) == 2*i). This has been very useful in physics.