Yeh, with modern screens you don't meed to worry about pixel density dots/inch or points/inch. An LCD screen will map an image pixel to pixel unless you zoom in or out or the image in some way or other. The screen itself will determine the density, so a 1080p 50" LCD will have a much lower dpi than a 32" LCD, but the mapping will still be 1px to 1px.
So as bigdave says, for a 1080p screen, create a 1920 pixels by 1080 pixel image.