i-adjective
difficult; hard to do
Formal or literary い-adjective. In modern Japanese it is especially familiar in written expressions such as 想像に難くない, “not hard to imagine”; ordinary conversation usually uses 難しい instead.
彼女がどれほど悔しかったかは想像に難くない。
It is not hard to imagine how frustrated she must have been.
The normal modern word for “difficult”; 難い is more formal or literary and is often limited to set written expressions.
A formal noun or な-adjective meaning “difficulty” or “difficult”; it sounds more administrative or abstract than 難い.
A homophone meaning “hard,” “firm,” or “stiff” in a physical or figurative sense; 難い uses a different kanji and means “difficult.”
The spelling uses 難, the kanji associated with difficulty. This distinguishes the “difficult” sense of かたい from homophonous spellings such as 固い, 硬い, and 堅い; no historical derivation is specified.