WOLFRAM|DEMONSTRATIONS PROJECT

Factoring Gaussian Integers

​
10i+18(7-2i)(-i)
3
(i+1)
Every nonzero Gaussian integer
a+bi
, where
a
and
b
are ordinary integers and
i=
-1
,
can be expressed uniquely as the product of a unit and powers of special Gaussian primes. Units are 1,
i
, -1,
-i
. Special Gaussian primes are
1+i
and primes
z
with
Re(z)>0
and
Re(z)>|Im(z)|
.