electromagnetic theory. (1) Vector analysis. It is ripe enough the electromagnetic theory described with the three-dimensional vector. However the theory has a questionable logicality, because the deduction of Maxwell’s equations is dealt with the participation of the current continuity equation. Logically, the electromagnetic strength determines the electromagnetic source via the Maxwell’s equations, and then the electromagnetic source concludes the current continuity equation. On the contrary, the electromagnetic source decides the displacement current in the Maxwell’s equations via the current continuity equation. This description method results in the problem of logic circulation. The puzzle urges other scholars to look for the new description method. (2) Real quaternion analysis. In the electromagnetic theory described with the real quaternion, it is able to deduce directly the electromagnetic field equations. But its displacement current’s direction and the gauge condition of field potential are respectively different to that in the classical electromagnetic theory. The limited progress arouses the scholar’s enthusiasm to reapply the complex quaternion to depict the electromagnetic theory. (3) Complex quaternion analysis. In the electromagnetic theory described with the complex quaternion, it is able to deduce directly the Maxwell’s equations in the classical electromagnetic theory, without the help of the current continuity equation. 