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Math Help - Question in section on rings and fields

  1. #1
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    Question in section on rings and fields

    Consider the set of numbers a + bi where a and b are elements of \mathbb{Z}/2\mathbb{Z}. i^2 = -1 which in \mathbb{Z}/2\mathbb{Z} is the same as 1. Write down all 4 elements of this set of numbers. Which elements have inverses?
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  2. #2
    MHF Contributor Swlabr's Avatar
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    Quote Originally Posted by Zennie View Post
    Consider the set of numbers a + bi where a and b are elements of \mathbb{Z}/2\mathbb{Z}. i^2 = -1 which in \mathbb{Z}/2\mathbb{Z} is the same as 1. Write down all 4 elements of this set of numbers. Which elements have inverses?
    What do you think the elements of the set are? What numbers are of the form a+ib where a and b are either 1 or 0?

    To find out which elements have inverses, square each element and see what happens.
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