There are several examples of actions the pigs take to control the other animals. Since you mention complacency, I am not sure what part of the book you are referring to. The animals were complacent in the beginning until Jones stopped feeding them. Then the animals broke into the store room and ate the food. When the men attacked them, they fought back and the men ran off. That was the first part of the revolution.
The pigs took advantage of propaganda and threats of violence to control the animals, I would argue that they wanted them to be complacent. In other words, it was to the pigs' advantage when the animals fought off the men, but complaceny was the goal after the pigs were in power. To control their subjects they used sneaky behavior such as scapegoating Snowball and changing the wording of the commandments, trading with the men and using more and more of men's trappings (hats, beds, books, alcohol and so on). They also executed "traitors" who had done nothing wrong.