Exhibit elements in a quadratic field having the same norm but which are not conjugate or associate

Exhibit elements in a quadratic field which have the same norm but which are not conjugate or associate.

Let $K = \mathbb{Q}(i)$. If $(a,b,c)$ is a Pythagorean triple, then $N(a+bi) = N(c)$, but $a+bi$ and $c$ are clearly neither conjugate nor associate. For instance, $\{3+4i,5\}$ and $\{5+12i,13\}$.