In recent years the theory of hypercomplex analysis has taken new directions towards more exotic examples such as the complex ternary case, in part due to possible applications in signal processing, physics, etc. The theory developed here is a particular case of the more general case discussed in a volume the author working on and a continuation of the real ternary analysis case developed earlier. We discuss several applications of the newly developed theory of ternary complex analysis. This work is created in collaboration with D. Alpay and A. Vajiac.