Learn Farsi: چند خوابگاه در این مجتمع است؟ - How many dormitories are in this complex?

The suffix ـگاه (-gāh) is a very common Persian derivational ending added to nouns or verb stems to indicate a place (and sometimes a time). Here, it attaches to خواب (sleep) to literally mean "sleeping place" or "dormitory". You have likely seen this same suffix in words like دانشگاه (university, "knowledge place") or فرودگاه (airport, "descending place").

Why is خوابگاه in the singular form when the English translation says "dormitories"?

In Farsi, the question word چند (how many) must always be followed by a singular noun. A common mistake for learners is to pluralize the noun to match English grammar, but in Farsi, you are literally asking "how many dormitory" (چند خوابگاه).

Since the English translation is "are", why does the sentence use the singular verb است (is)?

This happens for two reasons. First, because چند forces its noun (خوابگاه) to be singular, the verb naturally agrees with that singular subject. Second, even if the subject were grammatically plural, inanimate objects in Farsi generally take singular verbs anyway.

Is مجتمع (complex) also formed using a derivational place suffix?

Not a Persian one. مجتمع (mojtama') is an Arabic loanword that refers to a "complex" (like a building or residential complex) or a "gathering place". It is derived from the Arabic root ج م ع (j-m-'), which relates to gathering or bringing together. It is closely related to other common words you know, like (population) and (society).