Biquaternion representation of the spin one half and its application on the relativistic one electron atom

In this work we represent the $1\mathrm{/}2$ Spin particles with complex quaternions using a transformation to 2x2 matrices in order to obtain the Pauli matrices. With this representation we determine the states, rotation operators and the total angular momentum function in the complex quaternion space. Using this representation we work the solution for the relativistic hydrogen atom.