Xbox live on imac computer

Yes you can. However it doesn't just work due to compatibility issues. To do this you will need to partition the HDD. Here is a good article for details on how to do this:Partition
for iMac and Xbox

It depends on what you want to do with the connection.

If you want to stream media from your iMac to your Xbox console, you will simply need a DLNA compliant server that you can put on your iMac. For example
Serviio will do that.

If you want to stream gameplay from your Xbox One to your Mac, you will need to use Bootcamp to prepare room for a Windows 10 installation, get Windows 10 and install that on your iMac, and then use the Xbox App to stream your gameplay to your iMac running
Windows 10.

You’ll want to grab a micro-USB cable to hook your Xbox One or Xbox 360 controller up since Bluetooth is out. Luckily, there’s still a way you can get things working. It will require a bit more craftiness on your part, but it’s nothing you shouldn’t be able
to handle.

I don't think the OP is asking how to connect an Xbox controller to an iMac, they appear to be asking how to connect the console to it.

If they are indeed asking how to connect the console to the iMac to use its screen, then I'm sorry but that isn't going to work. The connectors on the iMac (Display port or HDMI) are
outputs only. This means that they can only be used to output the iMac screen on a external display, you can't input a video signal into the iMac screen.

i have this question also. can someone also tell me if a imac 21.5 inch would work with xbox one, i have a adapter for mini display port to hdmi, will it still work on imac?

No, that would not work as you cannot use the iMac itself as an external monitor. The iMacs only have external video output and no video input to use as a separate monitor.