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Math Help - Complex numbers

  1. #1
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    Complex numbers

    How do you show that cube roots of unity (the set of complex numbers which satisfy z^3=1) for a group?
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  2. #2
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    Quote Originally Posted by chmaths View Post
    How do you show that cube roots of unity (the set of complex numbers which satisfy z^3=1) for a group?
    What is a group?
    The operation in this group is multiplication.
    So show that axioms for a group are satisfied.
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  3. #3
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    1. associativity (of multiplication) holds for any subset of the complex numbers (because the complex numbers form a ring).

    2. what is the multiplicative identity of C? is it a cube root of 1? (don't over-think this)

    3. how many cube roots of 1 are there? you can use the fundamental theorem of algebra. (if z^3 = 1, then z is a root of x^3 - 1.

    how many roots can a cubic polynomial have at most?). besides the "obvious" root of x^3 - 1, (which being a difference of two cubes,

    you should at least be able to factor a little bit) what are the "other roots"? and what is the product of these "other roots"?

    how does this tell you we have inverses?
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