Chloe Makdad *Butler University*

**Faculty Sponsor(s): **William Johnston *Butler University*

A new root and ratio test for bicomplex power series produces the Bicomplex Extension Theorem, where any complex power series with positive radius of convergence R extends, via a simple change of the complex domain variable z to the bicomplex variable Z, to a bicomplex function analytic in a four real dimensional ball with the same positive radius R. In this way, any complex analytic function has a natural extension to a bicomplex analytic function.

Mathematics & Computer Science