In transactional analysis three broad ego states are defined. The parent, The child and The adult state. As the name suggests, each of these ego states has its own unique identity and every individual exhibits one or more of these ego states at a given point in time.
What is a transaction ? Put in simple words transaction is a relation, a communication established between two people. Each transaction essentially has two parts, one the stimulus and the other response. These transactions can happen between one ego state to the other.
The simplest form of transaction is the complimentary transaction. Here the person responding to another person who has triggered the response is in the same ego state as that expected by the stimulus. In other words, If a person talks to you as an adult, expecting an adult response, the person replying back also responds in the same ego state, thus complimenting the transaction.
Let us take an example to understand this better. A boss tells his sub-ordinate "This presentation needs re-work. You need to do this again and submit it by noon". This is essentially a parent ego and he expects a submissive response from his sub ordinate. His sub-ordinate responds saying "Yes sir. I understand. I will redo the entire presentation and give it to you by noon". Here the sub-ordinate is in the child ego state and accepts his mistake and agrees to his boss.
The above example is a typical complimentary transaction. Here the response (the sub ordinate) is in the ego state as expected by the stimulus (the boss). In a complimentary transaction it is easy to continue a conversation as the chances of conflict are minimal and a health dialogue can be established for a longer duration of time.