Complex Exponents and Group Theory

Abstract

SummaryThere is much confusion in the literature about the meaning of zw, where z and w are complex numbers with . For example, we are often told that (a number), but that ii is an infinite set. So which of these is true? Is zw a set or a number? It cannot be both, and here we suggest how the inconsistent use of the universal notation zw can be clarified and resolved by using elementary group theory.