Greetings again Fish153,
These two references have been extensively discussed earlier in this thread, by myself and a thorough presentation by a Trinitarian.
My position is that these two verses are part of a major theme in John's Gospel of whether Jesus is the Christ. The same words and language is used on a number of occasions concerning this theme:
John 1:19–20 (KJV): 19 And this is the record of John, when the Jews sent priests and Levites from Jerusalem to ask him, Who art thou? 20 And he confessed, and denied not; but confessed, I am not the Christ.
John 4:25–26 (KJV): 25 The woman saith unto him, I know that Messias cometh, which is called Christ: when he is come, he will tell us all things. 26 Jesus saith unto her, I that speak unto thee am he.
John 7:25–26 (KJV): 25 Then said some of them of Jerusalem, Is not this he, whom they seek to kill? 26 But, lo, he speaketh boldly, and they say nothing unto him. Do the rulers know indeed that this is the very Christ?
John 8:24 (KJV): I said therefore unto you, that ye shall die in your sins: for if ye believe not that I am he, ye shall die in your sins.
John 8:28 (KJV): Then said Jesus unto them, When ye have lifted up the Son of man, then shall ye know that I am he, and that I do nothing of myself; but as my Father hath taught me, I speak these things.
John 8:58 (KJV adjusted): Jesus said unto them, Verily, verily, I say unto you, Before Abraham was, I am he.
Also this has been discussed and John 1 is part of the theme that Jesus is the Son of God by birth, character and resurrection. These two themes are mentioned in his concluding comments:
John 20:30–31 (KJV): 30 And many other signs truly did Jesus in the presence of his disciples, which are not written in this book: 31 But these are written, that ye might believe that Jesus is the Christ, the Son of God; and that believing ye might have life through his name.
Kind regards
Trevor