Quaternions Algebra by Using Brackets of Complex Numbers | Asian Journal of Pure and Applied Mathema

Hamilton introduced quaternions and anti-quaternions in 1843, and they are crucial in practical mathematics and physics. Many academics have explored Quaternions in particular for computing the rotation of a point in space, and we will define them as (22) matrices form of complex numbers, or as vector form of a real number and three complex numbers (as generalisation of a complex numbers), or as (44) real matrix.

In this work, we provide these quaternions in a novel form that simplifies the calculus by employing complex number brackets, and then we investigate some of their properties. And rotations in complex numbers using this approach of brackets.

We also look at several types of quaternions and some basic algebraic features and geometric uses of them employing this complex number bracketing approach We can see that by writing a (44) real matrix in the form of brackets of complex numbers and performing mathematical operations over these brackets, the number of operations required in this case is less than in the case of classical matrices operations; additionally, this method simplifies and speeds up the calculations.

Please see the link :- https://globalpresshub.com/index.php/AJPAM/article/view/1434