i may play for a bit to see if there was some tactic that i didn't see. but i think resignation is reasonable. be sure to tell your friend that you want them to play their best and not go easy on you.
similiarly, i once blundered against my dad and made a chat comment imediately with "oops" or something and he offered to play a few fake moves to achieve "Takeback". i told him to take her and lost in two moves. much more fun that way.
If a friend and a much higher rated player and he is both. Did not take your Queen after a blunder in order to just keep game going would you resign? Yes it is a rated game.