wireless keyboard not seen by 2011 iMac

Try Apple's suggestions in Bluetooth: How to set up your Apple Wireless Keyboard - Apple Support

You may need a wired keyboard to carry out some of these steps. It's a good idea to keep a cheap wired keyboard and mouse or trackball as backups for a desktop Mac, because Bluetooth isn't completely reliable.

Step 1

If the keyboard is already paired with another device, remove that pairing.

Step 2

Follow the instructions inthese support articles:

How to set up your Apple Wireless Keyboard

Apple Wireless Keyboard: Difficulty during pairing process

Bluetooth devices become unresponsive

Step 3

The keyboard should pair automatically when you restart the computer. You may have to press and hold the power button on the right side of an Apple keyboard until the LED starts flashing.

Step 4

Reset the System Management Controller.

Step 5

Back up all data.

Triple-click anywhere in the line below on this page to select it:

/Library/Preferences/com.apple.Bluetooth.plist

Right-click or control-click the line and select

Services ▹ Reveal

from the contextual menu.* A folder should open with an item selected. Move the selected item to the Trash. You may be prompted for your administrator login password. Restart.

*If you don't see the contextual menu item, copy the selected text to the Clipboard by pressing the key combinationcommand-C. In the Finder, select

Go ▹ Go to Folder...

from the menu bar and paste into the box that opens by pressing command-V. You won't see what you pasted because a line break is included. Press return.

Step 6

See these support articles:

Bluetooth keyboard may not pair during Setup Assistant

Wi-Fi and Bluetooth: Potential sources of wireless interference

Bluetooth: Unreliable wireless performance may occur when USB 3.0 external devices are close

Step 7

Make a "Genius" appointment at an Apple Store, or go to another authorized service provider.