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m Removed one parenthetic interjection, as it gets a bit tiresome in the lead. The reader will have no difficulty figuring this one out. Also removed a "therefore". |
m Improved wording introduced a few days ago. |
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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 absolute value (Euclidean
:<math>N \left(a+bi \right) = a^2+b^2 = (a+bi)\overline{(a+bi)} = (a+bi)(a-bi).</math>
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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>
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