Advanced root

This note introduces a subscript notation for explicitly labeling the n distinct branches of the complex n-th root. The notation assigns a unique index m = 0, 1, ..., n-1 to each branch, making individual roots directly accessible without ambiguity. The principal root corresponds to m = 0 and recovers the classical n-th root. The non-negative real case and the square root case are treated as special instances. Several examples are provided, including an infinite nested radical evaluated using a non-principal branch. The subscript convention presented here is the author's own formulation, independently developed in July 2016.