Gaussian rational

In mathematics, the field (mathematics) of Gaussian rationals is the field Q( i ) formed by adjoining the imaginary number i to the field of rational number. It consists of the complex numbers of the form p  +  qi , where p and q are both rational, and is an example of a quadratic field.

The field of Gaussian rationals is neither ordered field nor complete. The Gaussian integers form the ring of integers of Q( i ).