I want to show that Chinese Remainder Theorem(CRT) has a unique solution over gaussian integers. But when I choose $x=4+5i$ and determine coprime modulo numbers $1+2i$ and $1+4i$, the simultaneous congruences
$4 + 5i \equiv - 1\,\bmod (1 + 2i)$
$4 + 5i \equiv - 1 + 2i\,\bmod (1 + 4i)$ is obtained. If I use CRT for modulo $1+2i$,$1+4i$ and remainders $-1$,$-1+2i$, I obtain $ - 2 + 2i \ne 4 + 5i$. What is the problem? When does a system have unique solution?