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Math Help - Minimum polynomial

  1. #1
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    Minimum polynomial

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

    Find the minimum polynomial for w over Q.

    I know that the minimum poly is the monic function f such that f(w) = 0.

    Nevermind, guys, I finally got the answer, is it p(x) = x^2 + x + 1?

    It looks so easy now, but it took me so long to get it. Thanks.
    Last edited by tttcomrader; January 26th 2008 at 11:54 AM.
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  2. #2
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    Quote Originally Posted by tttcomrader View Post
    Let  w = \frac {-1}{2} + \frac {3^{1/2}}{2}i

    Find the minimum polynomial for w over Q.

    I know that the minimum poly is the monic function f such that f(w) = 0.

    Nevermind, guys, I finally got the answer, is it p(x) = x^2 + x + 1?

    It looks so easy now, but it took me so long to get it. Thanks.
    The thing you do it write w = -\frac{1}{2} + i\frac{\sqrt{3}}{2} and square both sides and bring it to a form of a polynomial having rational coefficients.
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