grammar - Ai oboete imasu ka, what does "imasu" add here?

"Ai oboete imasu ka" is translated as "Do you remember love?", now Ai is love, oboete is remember and ka is the question marker, why do you need to add "imasu" to this phrase?

Answer

A note on translation

Expressing the same ideas in different languages inevitably results in all kinds of things that don't fit very well, if we try to look only at the individual words used in those expressions. This makes things quite difficult for the beginning learner, since we don't yet have a bigger-picture understanding of how a given language works.

So when we analyze how a given expression works in Language A, and we try to explain how that matches up with the expression in Language B that has roughly the same meaning, the explanation sometimes has to get pretty deep and nitty-gritty. :)

Background on the verb

The main verb here is the oboete (dictionary form: 覚える oboeru). The verb oboeru is often translated as "remember", but the aspect of the Japanese verb is a bit different.

Aspect is a tricky concept, and I won't get into it here -- read the Wikipedia article for the details.

In a simplified nutshell, the English verb "remember" does not express any change in state: the person doesn't necessarily change at all, comparing them before they remember something, and after.

The Japanese verb oboeru, however, does include a change in state, and this is closer to the English verb "memorize". In Japanese, you can say 漢字{かんじ}を覚える{おぼえる} to express the concept, "I memorize the kanji." The change in state here is that the person doesn't have the kanji in their head before they oboeru, and they do have the kanji in their head after they oboeru. A better translation thus might be "put something in mind".

Main question: what does the imasu do here?

The Japanese verb imasu (dictionary form: いる iru) is often translated as "am, is, be". This is usually a good fit -- 店{みせ}に行{い}きます, "I go to the store", vs. 店{みせ}に行{い}っています, "I am go​ing to the store". In most cases, imasu is used as an auxiliary (additional) verb to indicate the present progressive -- something is happen​ing.

However, verbs that indicate a change of state -- and this gets back to that tricky idea of aspect -- can take imasu to mean either 1) that the verb is happen​ing, or 2) that the change indicated by the verb has happen​ed and the new state is.

By way of example, 切{き}れる (kireru) is another of those verbs that indicates a change in state, and it basically means "to become cut". So 紙{かみ}が切{き}れる means "the paper becomes cut" → "the paper changes state from whole, to cut into pieces". 紙{かみ}が切{き}れている could mean "the paper is becom​ing cut", or it could mean "the paper has been cut" → "the paper is now in a state of having been cut". Context makes it clear which interpretation is more appropriate.

Looking back to the core verb oboeru, when we add imasu, we could mean that the person is memoriz​ing something -- this is a valid translation, but it depends on the context. The context in your example sentence suggests that the second interpretation makes more sense -- the person isn't in the process of memorizing love, or of putting love into their minds, but instead has put love in mind, i.e. they have it in their head → they remember it.