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Math Help - Units in Gauss integers ring

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    Units in Gauss integers ring

    Find units in a ring constituted by Gauss integers.

    So I know that Gauss integers are a+bi \ \ \ a,b \in \mathbb {Z} [/tex]

    Now, of course -1, 1, i, -i are units, but would 1-i,-1+i also be units? And are there anymore?
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  2. #2
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    Quote Originally Posted by tttcomrader View Post
    Find units in a ring constituted by Gauss integers.

    So I know that Gauss integers are a+bi \ \ \ a,b \in \mathbb {Z} [/tex]

    Now, of course -1, 1, i, -i are units, but would 1-i,-1+i also be units? And are there anymore?
    No. A Gaussian is a unit if and only if N(\alpha) = 1. Where \alpha = a+bi and N(\alpha) = a^2+b^2.
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