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Math Help - Show Z[w] is in form of a+bw

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    Show Z[w] is in form of a+bw

    Let <br />
w = \frac {-1}{2} + \frac {3^{1/2}}{2}i<br />

    Show that each element of Z[w] can be written in the form a+bw with a,b in Z
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  2. #2
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    Quote Originally Posted by tttcomrader View Post
    Let <br />
w = \frac {-1}{2} + \frac {3^{1/2}}{2}i<br />

    Show that each element of Z[w] can be written in the form a+bw with a,b in Z
    Work out the powers of w. You should find that w^2 = -1-w and w^3=1. Thereafter the powers of w repeat these values. It follows that any polynomial in w can be written in the form a+bw.
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