Complex modulus of Z[sqrt(-10)]

My lecture notes has the following.

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

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

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

$\displaystyle 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 $\displaystyle \mathbb{C}$? Can anyone pls show me the steps?

Re: Complex modulus of Z[sqrt(-10)]

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

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