What is the meaning of てこい?

Question

残りの夏休み遊べないのは残念だけど　ゆっくりしてこい!

So he tells his friend who is moving soon to another town

残りの夏休み遊べないのは残念だけど
it's too bad we won't be able to play anymore for the remaining days of summer, but

ゆっくりしてこい!

"Take it easy"? What meaning does てこい provide here?

Answer 1

This (-て)くる here means "and then come back". So the literal translation is "Have a relaxing time and come back".

You probably don't see the need for this kind of くる right now because saying "and then come back" is completely unnecessary in English in a situation like this. However, it's important in Japanese when describing doing something in a distant place and returning to your current location. In Japanese, just saying ゆっくりしろ in this context would sound awfully unnatural.

For more examples, see: What does やってくる mean in this sentence?

Conversely, a ryokan host commonly says ゆっくりしていってください to their guests, which literally means "Relax and then leave". In English, saying "and then leave" is not only unnecessary but even hostile, so it is usually just translated as "Make yourself at home" or something like that.

Answer 2

ゆくりして -> Take it slowly / Do it calmly / leisurely /...

こい -> 来る in imperative

Semantically, て form + こい = imperative of the verb in て form

The idea of the 来る imperative is to give emphasis to what is before it. Kind of like: "Bring it on!" [かかってこい]. The nuance is that kind of like a challenge. It really encourages the person to do the action. "Do it and I/we will be unfazed by it.", "Do it and I/we will be OK". It is considered rude or masculine.

It can also imply that you have to go to another location to do the action and come back as in (近くの店)買ってこい.

Do take it easy (and it will be OK)!