  We prove, using a theorem of Northcott, that if a number field K with s real
embeddings and 2t complex ones has a group of units U such that all elements in
U have all its complex conjugates of same absolute value, then one necessarly
has t = 1. This fact has an interesting implication in complex hermitian
geometry, namely it describes all Oeljeklaus-Toma manifolds carrying locally
conformally Kahler structures.
