Due October 25. Let R denote the set of complex numbers of the form a +...

Due October 25. Let R denote the set of complex numbers of the form a + b √ 3i, with a, b ∈ Z. Define N : R → Z≥0, by N(a + b √ 3i) = a 2 + 3b 2 . Prove: (i) R is closed under addition and multiplication. Conclude R is a ring and also an integral domain. (ii) Prove N(xy) = N(x)N(y), for all x, y ∈ R. (ii) Prove that 1, −1 are the only units in R.

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Colby Messinger answered 1 year ago

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