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We construct a class of finite rank multiplicative subgroups of the complexnumbers such that the expansion of the real field by such a group ismodel-theoretically well-behaved. As an application we show that aclassification of expansions of the real field by cyclic multiplicativesubgroups of the complex numbers due to Hieronymi does not even extend toexpansions by subgroups with two generators.

On expansions of the real field by complex subgroups