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Math Help - roots of i, polynomial

  1. #1
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    roots of i, polynomial

    Let alpha and -alpha be the square roots of i.
    Write down a degree two polynomial having alpha and -alpha as its roots. Then write down a degree four polynomial with integer coefficients having alpha and negative alpha among its roots. What are the other two roots of this polynomial.

    I don't know if I can't do this because I really don't understand what the question is asking me or if the question is just going straight over my head
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  2. #2
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    What about \displaystyle f(z) = (z - \alpha)(z + \alpha)?
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    I'm really sorry. I still don't get where to go.
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    The value \alpha=\cos\left(\frac{\pi}{4}\right)+i~\sin\left(  \frac{\pi}{4}\right) , that is one square root of \mathif{i}.
    Is \alpha a root of z^4+1=0~?
    What are the other roots?
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