A method is devised for calculating the antenna patterns of

-arm spiral or conical antennas and is applied specifically to the determination of the

and

patterns. These calculations are greatly facilitated, if not rendered practically feasible, by the use of bicomplex functions which are described. It is found that in the vicinity of the antenna axis, circular polarization is obtained in the

pattern regardless of the nature of the antenna structure if

, and in the

pattern if

; furthermore, each of these patterns is determined by the field at a single point.