Gaussian integer

We could say that a Gaussian integer is larger than another if its norm is larger, that is, if its distance from the origin is larger. That's all right, although it has the peculiarity that 5 is larger than -7 as an integer, but smaller than -7 as a Gaussian integer! In a way, this notion of larger makes more sense: shouldn't -7 be considered larger than 5?

2000, André Weilert, Asymptotically fast GCD Computation in ℤ[i], Wieb Bosma (editor), Algorithmic Number Theory: 4th International Symposium, ANTS-IV, Proceedings, Springer, LNCS 1838, page 595, We present an asymptotically fast algorithm for the computation of the greatest common divisor (GCD) of two Gaussian integers.

2008, Timothy Gowers, June Barrow-Green, Imre Leader (editors), The Princeton Companion to Mathematics, Princeton University Press, page 319, For example, in the ring of Gaussian integers, R_-1, we have the factorizations 2=(1+i)(1-i), 5=(1+2i)(1-2i), 13=(2+3i)(2-3i), 17=(1+4i)(1-4i), 29=(2+5i)(2-5i), ⋮ where all the Gaussian integer factors in brackets above are irreducible elements of the ring of Gaussian integers.