Learn Farsi: کجا می‌روی؟ من خدمت استاد می‌روم چون ایشان منتظر هستند. - Where are you going? I am going to see the professor because he is waiting.

This is the respect-plural taught in this lesson. When talking about an esteemed third person like a professor, Farsi speakers use the 3rd person plural pronoun ishân (instead of the singular u) and match it with a plural verb like hastand to show deference.

The first question is کجا می‌روی؟ (Where are you going?). Why is the intimate singular form used here?

The speakers are using the informal register with each other, implying the pronoun to (you, singular) by using the 2nd person singular verb ending -i. It highlights a contrast: they are casual with each other, but highly respectful when referring to the professor.

Why does the speaker say they are going خدمت استاد instead of using a standard verb for 'to see' or 'to visit'?

The word khedmat literally means 'service' or 'presence'. Saying you are going khedmat-e someone is a deferential Farsi idiom that means going to see them. It acts almost like a preposition of location here and perfectly matches the respectful tone of using ishân.