On distinct unit generated fields that are totally complex
  We consider the problem of characterizing all number fields $K$ such that all algebraic integers $\alpha\in K$ can be written as the sum of distinct units of $K$. We extend a method due to Thuswaldner and Ziegler that previously did not work for totally complex fields and apply our results to the case of totally complex quartic number fields. 
Daniel Dombek, Zuzana Mas\'akov\'a, Volker Ziegler
math.NT