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  1. #1
    Super Member
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    i

    Let i be the complex number (0,1)

    Show that i = (0,1) and (0, -1) are the only square roots of -1. Hint: Suppose that (x,y)(x,y) = (-1,0) and show that x = 0 and y = +-1. You can use the fact that, for real numbers, the only square roots of positive 1 are +-1. You also know that x^2 >= 0.

    I have no idea what to do...Any advice?
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  2. #2
    MHF Contributor
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    Quote Originally Posted by jzellt View Post
    Let i be the complex number (0,1)

    Show that i = (0,1) and (0, -1) are the only square roots of -1. Hint: Suppose that (x,y)(x,y) = (-1,0) and show that x = 0 and y = +-1. You can use the fact that, for real numbers, the only square roots of positive 1 are +-1. You also know that x^2 >= 0.

    I have no idea what to do...Any advice?
    Hi

    The rules of multiplication in \mathbb{C} are
    (x,y)(x',y') = (xx'-yy',xy'+x'y)

    Therefore (x,y)(x,y) = (x-y,2xy)

    Suppose that (x,y)(x,y) = (-1,0) then
    x-y = -1
    2xy = 0

    I think you can finish now
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