I'm using the wireless keyboard that came with my iMac with my iPad. No additional app required. I had to figure out how to pair it, having to turn off my computer, turn off the keyboard and then turn it back on before pairing with the iPad, but it's the same keyboard.
With the wireless keyboard just turn the bluetooth off on your iMac and keep on the Bluetooth on your iPad then pair by going to the Bluetooth section on the iPad and wireless keyboard should be there. No need to keep turning things off!