There's no need to contact Apple Support to locate your IMEI, you can find it right on your device.
FROM THE ABOUT MENU:
Tap to open Settings from your Home Screen.
Press to select General from the Settings menu.
Choose About from the General menu.
What is an IMEI Number
The International Mobile Equipment Identity (IMEI) number is a unique identification or serial number that all mobile phones and smartphones have. It is normally 15 digits long. GSM networks use the IMEI number to identify valid devices, and can stop a stolen phone from accessing the network.
Scroll down to find your IMEI number displayed.
FROM THE DIALER:
Tap to open Phone from your Springboard.
Press to select Keypad from the tabs at the bottom of the screen then input *#06#.
Your IMEI number will be displayed on the screen.
FROM THE SIM CARD TRAY:
Your IMEI will also be printed on the SIM tray as shown below.