Compliment - Compliment is a formal respect to you. Sometimes is also informal. It is out of courtesy which a person says or delivers to you so that he can make you a remark for something. It is something like saying 'good', 'great' or something like that.
Complement - Complement is something which completes you. Let's take an example. Take a mobile phone. Without a good sim-card, a mobile phone is of no use because with it, you won't be able to communicate with anyone.
So, here the sim-card is a complement for the mobile phone because it completes the mobile phone and makes it perfect at it's functioning.
1. I received good compliments from my girlfriend when I last sang a song for her.
2. My mother gave me good compliments for the food which I cooked.
3. I was rewarded with good compliments because of my work in ISC.
4. Sanjeev Sir is always loaded with good compliments because of the grade of work he does.
5. I must say that you were really looking beautiful, just a compliment darling.
1. The sim-card is a complement for the mobile phone.
2. Sam is my complement, without her, I am incomplete.
3. My mom is a complement for me, I feel really like something lacks in me when my mother is not with me.
4. My school addressed all of us as it's complement because, it says, we are important for them.
5. They look so beautiful with one another, really a good couple, complements for each other.