Simple question about finding roots of a polynomial

Question

What am I doing wrong here?

This is the denominator of one of my problems and I need to find the roots, so:

$6i-z^2+1 \to z=\sqrt{1+6i}$ and $z=-\sqrt{1+6i}$

$\therefore$ $(z+\sqrt{1+6i})(z-\sqrt{1+6i})$

But when I multiply them back together, I get

$$z^2-6i-1$$

, which doesn't match the original expression. I know I'm making a very simple mistake somewhere...

Answer 1

$$ (z+\sqrt{1+6i})(z-\sqrt{1+6i}) = z^2 - (\sqrt{1+6i})^2 = z^2 - (1 + 6i) $$

$$ -(-z^2+(1+6i)) = -[ 6i - z^2+1] $$