Manyetohydrodynamic equations representation with complex quaternions

This study aims to investigate the efficient representation of magnetohydrodynamic (MHD) equations using complex quaternions, which play an important role in mathematical physics, and how this representation can contribute to physical understanding. The basic properties of complex quaternions are studied and their algebraic structure and matrix representations are discussed in detail. This review provides an introduction to understanding the nature of complex quaternions before moving on to MHD equations. It then discusses how complex quaternions can be related to the equations of Magnetohydrodynamics. In this context, it describes the interactions between electromagnetic fields and fluid motion by considering the M.H.D. equations. The last part of the thesis shows how the M.H.D. equations can be represented using complex quaternions. It discusses the implications of this representation on the solution and physical interpretations of the equations and emphasizes the potential applications of complex quaternions.