There are two types of expressions that use “[V-te]+kuru/kimasu”, although it is usually “kimashita” for the second one;
(1) [V-te] + kimasu(来ます)
“kuru/kimasu” in this one means a physical movement, and usually the kanji(来) is used. The speaker takes an action described by [V-te], and then will come here.
1. Chotto Toire ni Itte Ki masu. (I am going to the restroom a while, and then coming back.)
(2) [V-te] + kimashita(きました)
“Kimashita” in this one means a change over time, usually change from past to present. And “Kimashita” is written in Hiragana.
2. Chichi no Kami ga Shiroku Natte Ki mashita. (My dad’s hair has come to be white.)
Since this is an expression of intermediate level, this post doesn’t deal with it much.
The exercise A3 of the section 43 in Minna no Nihongo is about (1). The following is example sentences of (1).
3. Chotto Ryou de Sato-san no Yousu o Mite Kimasu. (I am going to see how Sato-san is in the dormitory (and then coming back).)
4. Chotto Ie no Tojimari o Kakunin-shite Kimasu. (I am going for checking whether or not the doors are locked in my house (and then coming back).)
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This post was written with reference to the exercise A3 of Section43 in “Minna no Nihongo (2nd Edition)” published by “3A Corporation”
