The point is that the quaternions are an extemsion of the complex numbers - they are a larger set of numbers - just as the complex numbers are an extension of the real numbers. Within the set of real numbers -1 has no square root at all. Within the complex numbers -1 has two square roots. And within the quaternions -1 actually has infinitely many square roots. Hope that helps.

The point is that the quaternions are an extemsion of the complex numbers - they are a larger set of numbers - just as the complex numbers are an extension of the real numbers. Within the set of real numbers -1 has no square root at all. Within the complex numbers -1 has two square roots. And within the quaternions -1 actually has infinitely many square roots. Hope that helps.