I got Samsung SyncMaster 2343NW monitor from my friend. It has 2048x1152 native resolution. Is there a way to force monitor to 1920x1080 without making it all blurry? I have no idea how does that work, but my TV is 1920x1080 right? And it's not blurry when I connect my PC to it.
Not really. Is there any particular reason you need to? They are both 16:9 resolutions.
As a rule, you should use the resolution your monitor is meant to display, because if you don't the pixels of the output won't align with the physical pixels causing it to look fucked
So to summarise, just use 2048x1152 unless you have a very good reason not to.