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Verifying a subring?

  1. Mar 4, 2012 #1
    For [itex]\alpha = (1+ \sqrt{-3})/2 \in ℂ[/itex] and [itex]R = \{ x +y\alpha \, | \, x,y \in Z \}[/itex].

    How would you verify that R is a subring of ℂ? Everytime I multiply two 'elements' of R to check closure I get the negative complex conjugate of [itex]\alpha[/itex], I think I'm doing something wrong...

    Thanks!
     
  2. jcsd
  3. Mar 4, 2012 #2

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    Let's see...

    The negative complex conjugate of ##\alpha## is:
    $$-\overline{\alpha} = - \frac 1 2 (1 - \sqrt{-3}) = \frac 1 2 (1 + \sqrt{-3}) - 1 = \alpha - 1$$

    What exactly is the problem?
     
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