You can see your completed tasks either on the day they were completed or in the archive. You can also use the search for finding completed tasks.
Completed tasks in past days
Use the calendar icon in the left sidebar or the buttons to navigate to any day in the past and to see the tasks you completed on that day.
If you do not see your tasks there, the completed list is probably toggled off from the list. To show it hover your mouse to the right of the screen and click the completed section toggle button:
Completed tasks in the archive
The archive is where all your completed tasks are listed.
Use the menu at the top right to go to the archive.
In the "Archive & Stats" overlay make sure you are on the archive page (top left or use keyboard shortcut "A").
Search for completed tasks
You can search for a completed task or project by going to the archive overlay and clicking the search icon at the top right.
Filter and sort
In the search dialog you can filter and sort your completed tasks on the top right.
Find out when item was completed
Underneath each item in the search you can see when the item was completed.