  In classical electromagnetic theory, one formally defines the complex dipole
moment (the electric plus 'i' magnetic dipole) and then computes (and defines)
the complex center of charge by transforming to a complex frame where the
complex dipole moment vanishes. Analogously in asymptotically flat space-times
it has been shown that one can determine the complex center of mass by
transforming the complex gravitational dipole (mass dipole plus 'i' angular
momentum) (via an asymptotic tetrad trasnformation) to a frame where the
complex dipole vanishes. We apply this procedure to such space-times which are
asymptotically stationary or static, and observe that the calculations can be
performed exactly, without any use of the approximation schemes which must be
employed in general. In particular, we are able to exactly calculate complex
center of mass and charge world-lines for such space-times, and - as a special
case - when these two complex world-lines coincide, we recover the Dirac value
of the gyromagnetic ratio.
