# Is Chinese Remainder Theorem relevant here?

$\large{\begin{cases} Z &=& (q_{1})(1 - i) \\ Z &=& (q_{2})(1 - 2i) - i \\ Z &=& (q_{3})(1 - 4i) + 2 \\ Z &=& (q_{4})(3 - 2i) + 2i \\ \end{cases} }$

Let $$Z$$ be a Gaussian integer and $$q_{1}$$, $$q_{2}$$, $$q_{3}$$, & $$q_{4}$$ be the Gaussian integral quotients of the system above, what is the least value of $$| Z | ^{2}$$?

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