In 2000 Victor Lomonosov suggested a counterexample to the complex version of Bishop–Phelps theorem on modulus support functionals. We discuss $$c_0$$ -analog that example and demonstrate set sup-attaining functionals is non-trivial, thus answering an open question, asked in Kadets et al. (The mathematical legacy Lomonosov. Operator theory. Advances analysis geometry 2. De Gruyter, Berlin, 157–...