Alarm on ZTE Kis 3 doesn't seem to work when phone is off

[hairylichen]

I'm completely new to smart phones, so a total dummy. Got a ZTE Kis 3 a few days ago. I set the alarm to wake me up, switched the phone off and went to sleep. The alarm didn't sound in the morning. What did I do wrong? I've set the alarm before, and it does sound at the right time if the phone is on.