\textbf{S}^\prime ~.\end{aligned}$$

Comparing Eqs.(32)-(35) with the Maxwell’s equations in the classical electromagnetic theory states that those two field equations are equivalent to each other. It means that in the electromagnetic theory described with the quaternion, without the participation of the current continuity equation, it is still able to reason out the Maxwell’s equations in the classical electromagnetic theory.

\[sec:level1\]Conclusions and Discussions
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Applying the complex quaternion space, the paper is able to describe simultaneously the electromagnetic field equations and the gravitational field equations. The spaces of gravitational and electromagnetic fields both can be chosen as the quaternion spaces. Furthermore some coordinates of those two quaternion spaces and relevant physics quantities may be the imaginary numbers.

In the definitions of the quaternion operator, field potential, field source, radius vector, and velocity etc, the coordinates with the basis vector $\emph{\textbf{I}}_0$ or $\emph{\textbf{i}}_0$ are all imaginary numbers. However this simple case is still able to result in many components of other physics quantities to become the imaginary numbers even the complex numbers. In the definitions, only by means of the confinement of the component selection can we achieve the quaternion field theory which approximating to the classical field theory, enabling it to cover 