i purchased a new wireless full size keyboard. How do i sync it with my iMac?

Update your software and check your version of macOS

First, use Software Update to check for any new software your computer may need. After those updates are complete, check which version of macOS your computer has by choosing About This Mac from the Apple () menu.

Apple wireless keyboards

Magic Keyboard with Numeric Keypad

• Numeric keypad
• Lightning connector, built-in battery
• Requires macOS 10.12.4 or later

Magic Keyboard

• Lightning connector, built-in battery
• Requires OS X 10.11 or later

How to identify your Apple wireless mouse, keyboard, or trackpad - Apple Support

Magic Mouse 2, Magic Keyboard, Magic Keyboard with Numeric Keypad, Magic Trackpad 2

Follow these steps to set up your Magic Mouse 2, Magic Keyboard, Magic Keyboard with Numeric Keypad, or Magic Trackpad 2:

1. Connect a Lightning to USB Cable or a USB-C to Lightning Cable to the Lightning port on the device, and connect the other end of the cable to your Mac.
   Learn how to connect your Mac to a device with a Lightning port.
2. Make sure the device's power switch is in the ON position. (Green is visible under the switch when the device is on.)
3. The device appears in Bluetooth Preferences and automatically pairs with your Mac.
4. The Bluetooth Preferences window shows the connection status and charge level of your device. When the device is charged, unplug it for wireless use.

How to set up your Apple wireless mouse, keyboard, and trackpad - Apple Support

If you are on an older iMac that can only be upgraded to OS X 10.7.5 “Lion”, ( NOT Mountain Lion ), none of the newest Apple wireless input peripherals will work with this Mac.

You will need to return these and look for older wireless Apple Bluetooth peripheral input devices still compatible with older Mac OS X versions OR seek out third party wireless Bluetooth input peripheral devices that are compatible with your OS X version.

Sorry & Good Luck!