Did Jesus die physically?

I was watching the show 30 Days about a Christian living in a Islamic society, I listened to the agument of a Islam teacher about how God cannot die. I am trying to understand how it is not a contradiction for Jesus, who was god in flesh and spirit, to actually die in the flesh. I understand that he was resurrected(body and spirit) but it still means he was dead for a period of time. So did God or part of what is God actually die?