The paper determines the number of states in a deterministic finite automaton (DFA) necessary to represent “unambiguous” variants of the union, concatenation, and Kleene star operations on formal languages. For the disjoint union of languages represented by an m-state and an n-state DFA, the state complexity is mn - 1 for the unambiguous concatenation, it is known to be m2^n-1 - 2^n-2 (Daley et al. “Orthogonal concatenation: Language equations and state complexity”, J. UCS, 2010), and this paper shows that this number of states is necessary already over a binary alphabet; for the unambiguous star, the state complexity function is determined to be 3/8 2ⁿ+1. In the case of a unary alphabet, disjoint union requires up to 1/2 mn states, unambiguous concatenation has state complexity m + n-2, and unambiguous star requires n-2 states in the worst case.