¡Tranquilízate! - Calm down (Yes, it is imperative)
¡No te pongas así! - Don't be like this (like... don't be so bad, don't be so mad, etc) -- it's an imperative
¡Tranquilo! - it means "be relaxed", it's imperative as well. Use it for men.
For women you should say "tranquila"
For example:
1.
- Éste tipo besó mi novia. Voy a matarle. (This guy kissed my girlfriend. I am going to kill him)
- Tranquilizate y no haga esa estupidez. (Calm down and do not do that stupid thing)
2.
- María, quiero hablar contigo (María, I would like to talk to you)
- I do not want to see you ever again, you broke my heart and I am mad on you (No quiero verte núnca más, rompeaste mi corazón y estoy muy enojada contigo.)
- Anda, no te pongas así. Te juro que voy a cambiarme. (Com'on, don't be like this. I swear I'm going to change myself)
3.
Maestra,disculpe, no hice mi deber. ¿Puedo hacerlo para mañana? (Teacher, sorry, I did not do my homework. May I do it for tomorrow?)
- Tranquila, no pasa nada... claro que puedes. (be relaxed,never mind... Of course you can)
I hope it's clear now. If you have any further questions, feel free to ask me.
Have a nice day.