despair
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despair
A state of complete hopelessness and discouragement in which one no longer sees any way out.
In seiner Verzweiflung wusste er nicht mehr, was er tun sollte.
In his despair, he no longer knew what he should do.
'Verzweiflung' (despair) belongs to the verb 'verzweifeln' (to despair) and the noun 'der Zweifel' (doubt). The prefix 'ver-' here intensifies the idea of doubt to the point of hopelessness.
Er war am Verzweifeln, weil er keine Lösung fand.
He was despairing because he couldn't find a solution.
Common expressions are 'in seiner/ihrer Verzweiflung' (in his/her despair), doing something 'aus reiner Verzweiflung' (out of sheer desperation), or 'jemanden zur Verzweiflung bringen' (to drive someone to despair).
Aus Verzweiflung rief sie mitten in der Nacht ihre beste Freundin an.
Out of desperation, she called her best friend in the middle of the night.
'Verzweiflung' (despair) is a very strong word that describes a state of complete hopelessness. It is used more in serious or dramatic contexts.
Nach dem Verlust ihres Arbeitsplatzes ergriff sie die pure Verzweiflung.
After losing her job, she was seized by sheer despair.
hope
'die Hoffnung' and 'die Verzweiflung' are clear opposites. With 'Hoffnung', you still believe that something positive can happen. With 'Verzweiflung', you no longer see any way out and feel completely discouraged. So 'Hoffnung' fits when someone still has inner strength. 'Verzweiflung' fits when that strength is almost or completely gone.
Nach Stunden ohne Antwort rief er in seiner Verzweiflung noch einmal die Ärztin an.
After hours without an answer, he called the doctor once more in his despair.
Trotz der schlechten Nachricht verlor Maria die Hoffnung nicht.
Despite the bad news, Maria did not lose hope.