〜なければならない
must, have to
Verb ない-stem + なければならない / なりません
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なければならない means "must" or "have to": 薬を飲まなければならない, "I have to take my medicine". It's built from the ない form: ない → なければ ("if not") + ならない ("it won't do"). So, literally, "if I don't take it, it won't do".
Politely: なければなりません. なければいけません means the same and is equally common; both are accepted here.
It's long, so speech shortens it a lot: 飲まなきゃ, 飲まないと. You'll hear those far more often than the full form in anime and conversation.
For "don't have to", see the next point.
Register: なければいけない means the same; なきゃ is the casual shortcut.
Examples
明日は六時に起きなければなりません。
I have to get up at six tomorrow.
毎日、薬を飲まなければならない。
I have to take my medicine every day.
今日中に宿題をしなければなりません。
I have to finish my homework today.
明日までにレポートを書かなければならない。
I have to write a report by tomorrow.
すみません、もう帰らなければなりません。
Sorry, I have to go home now.