Welcome to iMore! It sounds like a hardware issue (which requires service by a technician) BUT you might want to try one or more of the following:
- Reset your device by holding the power button and home button down simultaneously until you see the Apple boot logo. If that doesn't work then try the next step.
- Remove your phone case and see if the purple spot disappears.
- Go to Settings > General > Reset > Reset All Settings.
- Restore your iPhone through iTunes. Set it up as a new device to weed out any possible software issues.
If all else fails, contact
Apple Support, visit an Apple Store, or go to a REPUTABLE repair shop.