I want to connect my full HD laptop running Windows 10 to and HD (1366×768) display. Will it work? My laptop has all connectors so that's not a problem.
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If it has the correspoding ports (such as HDMI, DVI, VGA...), any monitor should work.
Both Windows, as the rest of operative systems, and the monitor (unless it's very old) are capable of identifying the optimal resolution.
This means that, for example, if you have a 4K computer, it doesn't mean you have to use a 4K monitor. You just won't be able to enjoy as much definition as the computer is capable of offering, but it will definitely work.
There are two modes of operation when multiple displays are connected to a computer: screen duplication (mirroring) and desktop extension.
When using desktop extension mode, each screen acts as a completely separate one. You can have some windows on one and completely different ones on the other one. Their areas are virtually stitched on selected edges. Here's a screenshot from Windows display setting that shows how two screens are stitched, borrowed from this question:
The mouse pointer can be moved to the other screen through the stitched edge. This will work perfectly fine with screens of different resolutions, but the stitched edge will have to be shorter. This is the right mode if you're planning to use the other screen to enlarge available desktop space.
The other mode is mirroring or screen duplication. In this mode you have only one desktop that is visible on all screens. This is usually achieved by picking the highest resolution supported by all screens, but other resolutions can be configured too as long as they are supported on all screens. This will also work correctly for virtually any monitor, but as always with LCD screens, running them below their native resolution will negatively affect image quality.