Nooo dont unplug your computer! ... Turn it off at the switch (so unpowered) but you still want the earth connected so you can earth yourself. You may want to move it to another location with out carpet. Static electricity is not your friend. As you mention at the end of the video you want to make sure you put one hand on your computer case before you touch your ram and if able keep yourself in skin contact with the case of your computer. If your computer is unplugged from the wall it does nothing.
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