I live and work in Alaska where I am a resident but my family lives in Arizona do I have to pay taxes to Arizona

You pay in Alaska...

If you were not a resident at all of AZ in 2012, and have no AZ sources of income, then you do not owe and AZ income tax on your income. Assuming you are married and your wife is a resident of AZ you would file form 140NR (NR=non-resdident) for your AZ taxes; with this form you exempt all your non-AZ sources of income from AZ taxes.