Primfaktorzerlegung von 8 + 2 i {\displaystyle 8+2i} in Z [ i ] {\displaystyle \mathbb {Z} [i]} :
Wobei 1 + i {\displaystyle 1+i} und 4 + i {\displaystyle 4+i} prim sind und − i ∈ Z [ i ] × {\displaystyle -i\in \mathbb {Z} [i]^{\times }} (s. Diagramm).
![{\displaystyle \mathbb {Z} [i]}](https://wikimedia.org/api/rest_v1/media/math/render/svg/9ffa94e9e2e6d9e5e5373d5fafb954b902743fde)
![{\displaystyle -i\in \mathbb {Z} [i]^{\times }}](https://wikimedia.org/api/rest_v1/media/math/render/svg/da51bae3fe2915602eac109ac8faf72564d492e9)