Japanese verbs form ~te+oku (okimasu) and ~te+miru (mimasu)

In my previous posts on ~te (~て) form I've learned:

• simple command ~て
• polite affirmative ~て + ください (kudasai)
  
• continuous action~て+いる (iru)

Today I'll be studying ~te+oku (~て+おく) and ~te+miru (~て+みる).

Te Form + oku, okimasu

~て+おく oku: It means "will do certainly", "do in advance".
~て+おきます okimasu same but polite.

By itself, おく oku means "to put," but after a verb in the Te Form it means "will certainly do (that verb).

You may ask what's a difference between しておく shite oku and plain する suru? Both are "will do".

The answer is that any verb ~te+oku means that someone will definitely do that "verb~ておく" right away or in the very near future. It has a "will go ahead and do" kind of feeling to it. And this will be done in a short time.

• 待っておきる matte oku: "I will be waiting (definitely)"
• お弁当を作っておいた obentō o tsukutte oita. (I've made a boxed lunch (for later).)

The "e" in "te" often disappears, so

• 作っておいた tsukutte oita becomes 作っといた tsukuttoita.

More sentences:

• Ron ni denwa shite oku. (I'll call Ron.)
• Mado o akete oku. (I'll open the window.)
• Kasa o katte okimasu. (I'm going to buy an umbrella.)
• Kanojo ni ki o tsukeru you ni itte okimasu. (I'll tell her to be careful.)
• Shukudai o shite okimashita. (I [went ahead and] did my homework.)

The te + oku is usually compressed into something that sounds like "toku." For example, most native speakers would say the last example above so that it sounds like:

• Shukudai shtokimashita.

That's what you would actually hear.

Te Form + miru, mimasu

In English you say sometimes "I'll see if I can...," meaning that you would a try. Same in Japanese, miru means "to see," and you put the verb in the Te Form adding miru.
みます mimasu same but polite.

• 待ってみる matte miru: "I will see if I can wait"
  
• Kono kanji o yonde miru. (I'll try to read these kanji.)
• Kono atarashii PC o tsukatte miyou. (Let's give this new PC a try.)
• Sushi o tabete minai no? (Won't you try some sushi?)
• John ni hanashite mimasu. (I'll try to talk to John.)
• Kare ni denwa shite mimashita ga, rusu deshita. (I tried calling him, but he wasn't in.)

So, I've learned two more things to do with ~te verb form:
~te+oku - "definitely will ~verb".
~te+miru - "will try to~verb".