In computer graphics, Ken Shoemake formulated two ways for handling interpolation between them, one called Squad and another an adaptation of Bezier curves called a Slerp.  
The conjugate of these objects can be found by simply inverting the sign between all four terms.  In computer graphics, Ken Shoemake formulated two ways for handling interpolation between them, one called Squad and another an adaptation of Bezier curves called a Slerp.  One way to create them is to use the Cayley-Dickson construction.  The cross product of these quantities is sometimes referred to as the odd product, while one mechanism to do non- commutative multiplication with them makes use of the Grassman product. Unlike their matrix equivalents, they do not run into the problem of Gimbal Lock where a degree of freedom is lost.  Their formulator identified four rules that they must follow, such as the requirement that the individual square of the i, j, and k components all equal negative one.  FTP, identify these extensions to complex numbers formulated by William Rowan Hamilton that are useful in doing rotations.
The conjugate of these objects can be found by simply inverting the sign between all four terms.  
{Quaternions}