Gaussian integer

A Gaussian integer is a complex number a+bi where a and b are integers. 

The Gaussian integers are members of the imaginary quadratic field Q(sqrt(-1)) and form a ring often denoted Z[i], or sometimes k(i). The sum, difference, and product of two Gaussian integers are Gaussian integers, but (a+bi)|(c+di) only if there is an e+fi such that
(a+bi)(e+fi) = (ae-bf)+(af+be) i = c+di
(Shanks 1993).
Gaussian integers can be uniquely factored in terms of other Gaussian integers (known as Gaussian primes) up to powers of i and rearrangements.
The units of Z[i] are ±1 and ±i.
One definition of the norm of a Gaussian integer is its complex modulus
|a+ib| = sqrt(a^2+b^2).