It is typically defined as a solution of the quadratic equation , or equivalently, . Since this is not possible using real numbers, the solution is simply assumed to exist. By the usual understanding of the square root, the solution could be either of or . However, because the square root of a negative number is undefined in the real numbers, there is no way to distinguish between these two values. Fortunately, one need not decide which value "really" represents the imaginary unit, since all mathematical statements are just as valid when is replaced by .