I noticed many i-adjectives ending with く. I need to know why that happens.



Simply because that is how you use i-adjective.


-> tall
くない -> not tall
くなる -> become tall


すてき -> lovely
すてきじゃない -> not lovely
すてきになる -> become lovely


Basically, changing the い to a く turns the adjective into an adverb.

[速]{はや} = quick
[速]{はや} = quickly

As mentioned by this answer, this is also used to make the negative form of い adjectives:

[小]{ちい}さ = small
[小]{ちい}さくない = not small


Specifically, what's happening is that you're going from the adjective form to the adverb form. This can seem a bit weird when you think you're just trying to make a negative form or something, but that's how it works - roughly speaking, you're going from "takai" = "tall" to "takaku nai" = "not in a tall fashion" = "not tall".

i-adjectives behave a bit more like verbs in their conjugations, while na-adjectives behave a bit more like nouns, in that when you do stuff with an i-adjective you directly mess around with the ending, while with na-adjectives you leave the word untouched and just use particles and verbs to do all the heavy lifting.

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