paper discussed only the electromagnetic field equations and the gravitational field equations etc described with the complex quaternion, and the equivalent transformation of those field equations into that in the three-dimensional vector space. However it clearly states that the introducing of the complex quaternion space is able to availably describe the physics features of electromagnetic and gravitational fields. This will afford the theoretical basis for the further relevant theoretical analysis, and is helpful to apply the complex quaternion analysis to study the angular momentum, electric/magnetic dipole moment, torque, energy, and force etc in the electromagnetic and gravitational fields.

The author is indebted to the anonymous referee for their valuable and constructive comments on the previous manuscript. This project was supported partially by the National Natural Science Foundation of China under grant number 60677039.

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