This is the 2079th most frequent Polish word.
nadziei
"Hope" (genitive or dative form of "nadzieja").
Here, 'nadziei' is the genitive singular form of the noun 'nadzieja,' used to express quantity or possession of 'hope.'
Mam w sercu wiele nadziei.
I have much hope in my heart.
In this case, 'nadziei' appears in the genitive singular form, part of the negation of 'to lose' with reference to 'hope.'
Nie tracimy nadziei na lepsze jutro.
We do not lose hope for a better tomorrow.
Here, 'nadziei' is used in the genitive plural form to describe the object of our aspirations or hopes.