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of course. you don't need an i7 for that.
pretty much every intel mac mini is capable of 1080p.
 
They don't even break a sweat with a 1080p monitor. Just an FYI....it doesn't matter if it's a 22" or 30" monitor....if they're both 1080p the Mini has to output the same number of pixels - it's just the size of those pixels is different on the respective monitors - and the Mac doesn't control that.
 
The video card should have no issue with 27" monitors. I have mine attached to two 23" monitors and I don't think the output is that much higher on the video card. If you get above that, then it might be tricky without daisy chaining TB displays.
 
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