Do I need to have my computer in the same location to use Apple TV and AirPlay my i phone to my tv ?
To use Airplay your devices need to be on the same network.
The iPhone will Airplay to AppleTV without needing the computer on, but must be on the same network.
The computer works via Home Sharing separately to share compatible iTunes content or photos.
Airplay mirroring is available on modern Macs with Mountain Lion also.
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