Have you forgotten?

Have you forgotten?
 

Do native speakers say this?:

-Have you forgotten I am the chairman?

It seems unlikely, because at the time the listener gives a reply, he must have been reminded, so the grammatically required answer

-Yes, I've forgotten

is not logical.

The question contains phrasing that is commonly used.

The answer you have described as 'grammatically required' is grammatically correct, but certainly not required. In fact, it would be considered an impertinent answer.

Here are some likely responses.

"No."
"No, I haven't."
"No, I haven't forgotten."

Thank you, Rusty.

==========================

A detective said to his captive:

-You forget that we know nothing of all this; we have not heard your story, so we cannot tell how far justice could have been done on your side.

If the captive gives an answer, it should be, according to the tense required by FORGET, 'yes, I forget that', but the act of forgetting is past, would it be better to use YOU FORGOT THAT WE ....?

Have you forgotten? is high register English
You can also say did you forget?
I think it's standard English interrogative form
You forgot that.....? is blunt sounding, like a cop interrogating a suspect, perhaps implying disbelief.

It is quite correct to state 'you forget that ...'. It would not be proper to say 'you forgot that we ...'. A question isn't being asked. "You've forgotten" could be used.

The prisoner doesn't need to proceed with any form of 'forget'. He or she would be more concerned with the fact that no one knows his/her story and would ask permission to relate it.

By the way, 'how far justice could have been done on your side' is not quite right.
Justice can be on one's side, but it cannot 'do' on one's side.
There is an idiomatic expression 'do justice'. This may be used as 'could have done justice' or 'could have been done justice', but 'how far' and 'on your side' are out of place. So, assuming the author meant to say 'be' on one's side, the statement should have been "... how much justice could have been on your side."

Thank you, Rusty and Poli. Your answers give me tremendous confidence. I hope I can continue to learn English from you both.