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Math Help - Complex modulus of Z[sqrt(-10)]

  1. #1
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    Complex modulus of Z[sqrt(-10)]

    My lecture notes has the following.

    Consider the integral domain \mathbb{Z}[\sqrt{-10}] = \{ x + y \sqrt{-10} : x,y \in \mathbb{Z} \} and the equation

    7 = (x + y\sqrt{-10}) (u + v \sqrt{-10}) for some x,y,u,v \in \mathbb{Z}.

    Taking the modulus (in \mathbb{C}) of both sides and squaring we get

    49 = (x^2 + 10 y^2) (u^2 + 10 v^2) .

    My question is: how do we get the above equation by taking modulus in \mathbb{C}? Can anyone pls show me the steps?
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  2. #2
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    Re: Complex modulus of Z[sqrt(-10)]

    I am sorry for this dumb question, I haven't played with complex numbers for a while.

    x + y\sqrt{-10} = x + i y \sqrt{10}
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