[est]

> anything you can accomplish with quaternions were better accomplished with vectors of complex numbers

What about octonions? Are they even less useful?

[hanche]

The octonions aren’t even associative, making them less “natural” and harder to work with.

But quaternions are quite useful for working with rotations in three dimensions. To be very technical, the unit imaginary quaternions form a double (universal) cover of the rotation group SO(3).