Trinity Doctrine: One divine Being yet three Persons.
Christology: Christ had two natures; God and man
Three Persons; one of whom was both God and man.
The nature which was man died but God did not die. The proof is that God resurrected him.
John 2:19 Jesus answered them, “Destroy this temple, and in three days I will raise it up.”
Fully grasping the intricacies of the Trinity and the Incarnation are beyond our mortal minds, though.
By the way a 15 year old asked me some of these same questions. He was being attacked by Muslim classmates who asked a similar question. The fact that we can't totally understand it points to the marvelous wonder of the Trinity doctrine and also the Incarnation. We can state what the Bible says about it, but totally comprehending how it can be is impossible for us.
This topic was discussed in the Bible study room the other night. Someone remarked that God is a man. I know Christ is a man, and Christ is also God, but to state that God is a man is counter-scriptural. However, it seemed as if much of the room agreed with this statement!
You might want to read Forgotten Trinity by James White on this topic. It's the best laymen level book on the topic.