In this paper, we first introduce a lower bound technique for the state complexity of transformations of automata. Namely we suggest first considering the class of full automata in lower bound analysis, and later reducing the size of the large alphabet via alphabet substitutions. Then we apply such technique to the complementation of nondeterministic \omega-automata, and obtain several lower bound results. Particularly, we prove an \omega((0.76n)^n) lower bound for Büchi complementation, which also holds for almost every complementation or determinization transformation of nondeterministic omega-automata, and prove an optimal (\omega(nk))^n lower bound for the complementation of generalized Büchi automata, which holds for Streett automata as well.