it's written 깜짝이야 it doesn't have any relation to 갑자기

"you scared me to death" => 너 때문에 너무 놀랐다 / 너 땜에 가슴이 철렁했어 / 너 땜에 간 떨어질 뻔했어. - 가슴이 철렁하다: My heart sank/dropped. 철렁하다: literally "(a liquid) shifts/splashes" (mimetic/onomatopoeic), - 간 떨어질 뻔하다: My liver(간) almost(뻔하다) dropped(떨어질). ~ㄹ 뻔하다: almost did / came close to ~ing. "kamchakya!" == 깜짝이야. 깜짝 is a mimetic word describing the way you are startled. - 깜짝 놀랐어: I was startled. I was greatly surprised. - 깜짝이야: Gee! (That startled me.). 갑자기 is an adverb for "suddenly", "all of a sudden", unrelated to 깜짝이야.