This is the 14154th most frequent Russian word.
определенной
"Definite" or "specific."
The word 'определенной' is used here to describe the quality of 'сложности' (complexity), emphasizing that it possesses a specific and noticeable attribute.
Я нашел решение этой задачи с определенной сложностью.
I found the solution to this problem with definite complexity.
In this sentence, 'определенные' refers to 'права и обязанности' (rights and responsibilities), meaning that these rights and responsibilities are specific, defined, or recognized.
Каждый человек имеет определенные права и обязанности.
Every person has certain rights and responsibilities.
Here, 'определенная' describes 'уверенность' (confidence), implying that her confidence is of a certain degree or nature, distinct and identifiable.