Depending on how long the monitor you use has been connected to your computer, it is likely that when it detects that there is no activity in the CPU after a while it will turn off the monitor directly. In the old days, when most computers used the VGA connection it was done automatically, but with the HDMI connection that has changed and not for the better.
Although it is true that the HDMI connection allows us to make use of the monitor's speakers, it does not detect when we have turned off the computer or when we have closed session for, after a while or immediately, turn off the monitor, as was the case with CRT monitors with a VGA connection.
Despite all the news that has come from the hand of Windows 10, the Microsoft platform does not offer us any option that is responsible for turning off the monitor when we turn off the computer or when we log out, for which we are forced to resort to third-party applications.
Display Power Off is a perfect application to be able to configure that our computer is in charge of turning off the monitor when it has after the specified number of minutes after which we want the monitor to turn off.
This little app, we can also configure it for when screensaver starts up, a clear indication that we are not going to use the computer for a while, so the best we can do is turn off the monitor while the computer also goes to sleep once the set time has elapsed.
If we do not want to use a third-party application that is responsible for turning off the monitor automatically, we can choose to do it manually or program the monitor or TV to turn off automatically after a while by default, although this option is not available on all models.