If you declare it at the customs office of the airport you leave from, you will get a document which you can show the local "aduana" here upon arrival. Just by declaring all your valuables, you will eliminate any and all problems. This declaration serves the purpose of being able to take anything back, hassle free, when you return home. (But if you never return those items, nobody cares.)
Of course, this is valid if you come in on a foreign passport, as a tourist or maybe temp resident. Either way, once you enter it, if they don't tag it onto your PP, you can sell it here when you want to. Some people say they had their passport marked and so they had to re-export the item, as they left the country.
With the customs declaration you don't even need the invoice.
When you leave Argentina with whatever valuables-electronics, you shoukd do the same, but in reverse. (Declaracion de Aduana) If they don't record the serial number of a gadget, you can bring back a similar, yet newer model fitting the same description.