At this link, about half way down the page, there is an equation I don't understand
http://physicsforgames.blogspot.com/2010/02/quaternions-why.html
This is the equation. $$VV† = -x^2I^2 - y^2J^2 - z^2K^2 - xy(IJ + JI) - xz(IK + KI) - yz(JK + KJ)$$
How is this equation created? Is the cross symbol denoting + or -?
It's just expanding out the product of $V = x I + y J + z K$ and $V^\dagger = -x I - y J - z K$ term-by-term. We assume the usual distributive laws hold, but $I, J, K$ don't necessarily commute with each other.