Quaternion Negative Unity

Question

I'm reading Hamilton's Paper on Quaternions. Found here http://www.emis.de/classics/Hamilton/OnQuat.pdf. On page 5, the first statement of 7, says that there are only two different square roots of negative unity. I tried googling and I can't find what negative unity means. Can any one shed some light on this?

Thanks

Answer 1

He means that in complex arithmetic there are two square roots of negative one. The complex unit $i$ and $-i$ both square to $-1$.