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Math Help - Help with a multiplication table...

  1. #1
    Junior Member ginafara's Avatar
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    Help with a multiplication table...

    I need help with a multiplication table for Z_{2}[i] = {\{a+bi|a,b \in Z}\}

    I know the elements are {0, 1, i, i+1} for addition, are the multiplication elements the set \{0}?

    Also, I can't figure out how to determine i*i &  i(i+1)

    I have only had experience with modular arithmetic in {Z}

    any explaination would be appreciated. Thanks in advance.
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  2. #2
    Forum Admin topsquark's Avatar
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    Quote Originally Posted by ginafara View Post
    I need help with a multiplication table for Z_{2}[i] = {\{a+bi|a,b \in Z}\}

    I know the elements are {0, 1, i, i+1} for addition, are the multiplication elements the set \{0}?

    Also, I can't figure out how to determine i*i &  i(i+1)

    I have only had experience with modular arithmetic in {Z}

    any explaination would be appreciated. Thanks in advance.
    The multiplicative group is the same as the group itself. (Otherwise it would not be closed.)

    As so ii^2, what is -1 in your group? It is the additive inverse of 1, so
    1 + x = 0

    1 + a + ib = 0

    a = -1, b = 0

    Since this is based on Z_2,
    x = -1 \equiv 1

    You can do the same thing with i(i + 1) = -1 + i \equiv 1 + i.

    -Dan
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