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Note that when they are considered within the [[complex plane]] the Gaussian integers may be seen to constitute the 2-dimensional [[integer lattice]].
The [[Field norm|''(arithmetic or field) norm'']] of a Gaussian integer is the square of its (Euclidean) norm as a complex number and a [[natural number]] defined as
:<math>N \left(a+bi \right) = a^2+b^2 = (a+bi)\overline{(a+bi)} = (a+bi)(a-bi).</math>
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