"I am extremely tired."
Translation:제가 굉장히 피곤해요.
What is the significance of using 제가 instead of 저는 in this phrase? Does it need to be 제가 or would 저는 work too?
Both work, but they are different.
"제가 굉장히 피곤해요." can be an answer to the question "Who is tired?" i.e. the subject could have been anyone.
"저는 굉장히 피곤해요." can be an answer to the question "How are you?" i.e. the listener could expect the subject would be 저, thus it is followed by the topic particle.
This curious mix of polite and impolite versions of the language will never cease to amaze me... will I ever get them right?!