P10.2. Let w := }(−1 + √√3i) € C be one of the complex roots of the polynomial x² + x + 1 E in C[x]. Prove that the commutative domain Z[w] := {a + bw | a, b € Z} C C is a Euclidean domain with the function v: Z[w] →N defined by v(a + bw) = a²-ab+b².

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