  Complex geometry represents a fundamental ingredient in the formulation of
the Dirac equation by the Clifford algebra. The choice of appropriate complex
geometries is strictly related to the geometric interpretation of the complex
imaginary unit $i=\sqrt{-1}$. We discuss {\em two} possibilities which appear
in the multivector algebra approach: the $\sigma_{123}$ and $\sigma_{21}$
complex geometries. Our formalism permits to perform a set of rules which
allows an immediate translation between the complex standard Dirac theory and
its version within geometric algebra. The problem concerning a double geometric
interpretation for the complex imaginary unit $i=\sqrt{-1}$ is also discussed.
