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(Where the overline over "a+bi" refers to the [[complex conjugate]].)
The norm is [[completely multiplicative function|multiplicative]], since the
:<math>N(z\cdot w) = N(z)\cdot N(w).</math>
The latter can also be verified by a straightforward check. The [[unit (ring theory)|unit]]s of '''Z'''[''i''] are
==As a principal ideal ___domain==
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