  Using an extension of the abundancy index to imaginary quadratic rings that
are unique factorization domains, we investigate what we call $n$-powerfully
$t$-perfect numbers in these rings. This definition serves to extend the
concept of multiperfect numbers that have been defined and studied in the
integers. At the end of the paper, as well as at various points throughout the
paper, we point to some potential areas for further research.
