Split quaternions are noncommutative and contain nontrivial zero divisors. Generally speaking, it is difficult to solve equations in such an algebra. In this paper, by using the roots of any split two real nonlinear systems, we derive explicit formulas for computing x2+bx+c=0 quaternion

Quaternions have long been integral to the field of computer graphics, due to their minimal and robust representation of rotations in three dimensional space. Dual quaternions represent a compact method of representing rigid body transformations (that is rotations and translations) with similar interpolation and combination properties. By comparing them to two other kinds of rigid transformatio...

In this paper, we express De Moivre’s formula for split quaternions and …nd roots of a split quaternion using this formula. MSC 2000 : 53B30, 15A66.

must be the field, two copies of the field, the split quaternions, or the split octonions. There is a natural q-version of the composition property that the algebra Oq of quantum octonions is shown to satisfy (see Prop. 4.12 below). We also prove that the quantum octonion algebra Oq satisfies the “q-Principle of Local Triality” (Prop. 3.12). Inside the quantum octonions are two nonisomorphic 4-...

In this communication, introduce the split Mersenne and Mersenne-Lucas hybrid quaternions, also obtaining generating functions Binet formulas for these quaternions investigating some properties among them.