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Math Help - Field extension question

  1. #1
    Junior Member
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    Field extension question

    I have this kind of problem in which I need help:

    Let S \subseteq \mathbb{C} be a subfield. Show that S is the field extension of \mathbb{Q}, in other words, show that \mathbb{Q} \subseteq S.

    Any help would be great.
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  2. #2
    MHF Contributor FernandoRevilla's Avatar
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    Hint:

    1\in S implies 1+\ldots +1\in S , -(1+\ldots+1)\in S and 0\neq x\in S\Rightarrow x^{-1}\in S .

    Could you continue?
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