Important note: If you remember the position of your application and shutdown and then start up again at that position, keep in mind that the user's monitor configuration may have changed while your application was closed.
Laptop users, for example, frequently change their display configuration. When docked there may be a 2nd monitor that disappears when undocked. If the user closes an application that was running on the 2nd monitor and the re-opens the application when the monitor is disconnected, restoring the window to the previous coordinates will leave it completely off-screen.
To figure out how big the display really is, check out GetSystemMetrics.