Are these phrases common in modern German?
Do you use the phrases below?
- "Gestatten Sie mir, Ihnen meinen Freund vorzustellen"? (when you want to introduce somebody to somebody);
- "Gestatten Sie, dass ich mich vorstelle" (when you want to introduce yourself).
That highly depends, whether you're familiar with the person you're addressing, or whether you're rather wanting to be formal.
Both sentences of course can be used, but only in a highly formal manner. The first sentence would be used by someone to introduce their friend to the other person they're talking to.The second one would be the actual friend then taking over and responding.
The first one I could imagine could also go along the lines of:
"Dürfte ich Ihnen meinen Freund vorstellen?"
(Hearing both sentences, I instantly need to think of one of those fine dinner parties of really high business men.. everyone dressed up in suits, with a glass of champagne in their hands.So I wouldn't talk of a "common" use, but that might be a matter of age.)