What is the square root of $3 + 2\sqrt{10}i$? I need to compute the square root of $3 + 2\sqrt{10}i$.
I know how to solve it, but for some reason I'm not getting the correct answer. I attempted to solve it like this: 
$$
  \sqrt{3 + 2\sqrt{10}i} = x + iy
    \quad \longrightarrow \quad
  3 + 2\sqrt{10}i = x^2 - y^2 +2xyi
$$
and so forth, but my answer isn't correct.

$$ \sqrt{3 + 2\sqrt{10}i} = x + iy
$$
$$ 3 + 2\sqrt{10}i=x^2 -y^2 +2ixy $$
$$ x^2 -y^2 =3$$
$$ 2xy=2 \sqrt{10}$$
$$( x^2 + y^2 )^2= ( x^2 - y^2 )^2 +2xy $$
$$ x^2 + y^2 =7$$
$$ x^2 -y^2 =3$$
