You may know the German phrase Halt die Ohren steif, which is the equivalent of "Keep your chin up." These are tough times, and even if we generally are able to do this, it's sometimes hard not to complain about our current circumstances or the things we might be missing out on.
The most common verb for "to complain" in German is the reflexive verb sich beschweren. You can see in the second example below that it is used with the preposition über and the accusative.
Was ist los?
What is going on?
-Ach, nichts. Passt schon. Ich will mich nicht beschweren.
-Oh, nothing. It's OK. I don't want to complain.
Caption 29, Die Wohngemeinschaft - Probleme
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Ich habe mich bei ihm über meinen Nachbarn beschwert.
I complained to him about my neighbor.
Caption 30, Nicos Weg - A2 Folge 14: Nachbarschaft
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You may also see the verbs klagen and reklamieren. The verb klagen is also used in a legal context and means to file a lawsuit against someone.The verb reklamieren is particularly used for customer complaints (die Reklamationen), for example if an item is defective.
Wenn Kinder über Kopf- oder Bauchschmerzen klagen,
If children complain about head- or stomachaches,
nicht mehr zur Schule gehen wollen und sich zurückziehen,
no longer want to go to school and withdraw,
dann sollten Eltern hellhörig werden.
then parents should listen up.
Captions 28-30, Mobbing in der Schule - Mehr als Streit
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Vielleicht reklamiert sie was.
Maybe she's issuing a complaint.
Caption 12, Großstadtrevier - Nicht mit mir
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A common slang term for "to complain" is meckern. This verb actually means to bleat like a goat, but is used to express whining or grumbling.
Und daran gibt es nichts zu meckern.
And there's nothing to complain about there.
Caption 25, Die letzten Paradiese - Die Schönheit der Alpen
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Von uns Westberlinern wird gesagt, dass wir nur meckern,
People say about us West Berliners that all we do is complain,
aber die meckern ja nur noch mehr.
but they just complain even more.
Captions 51-52, Heute-Show - 30 Jahre Mauerfall: So feiern die Deutschen ihre Einheit
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Further Learning
Practice using the verb sich beschweren in various tenses, and don't forget to alter the reflexive pronoun. You can search for the infinitive sich beschweren and the participle beschwert on Yabla German to find further examples.