 Quadratic integers are generalizations of the Gaussian integers in which the imaginary unit "i" is replaced by a number .Thus, they have the form , where and are integers and has one of two forms, depending on a parameter .If does not equal a multiple of four plus one, then

If, however, "D" does equal a multiple of four plus one, then

If the function corresponds to a norm function, such as that used to order the Gaussian integers above, then the domain is known as "norm-Euclidean".