I just read this lesson on imabi and i'm confused.
"To make a polite negative phrase, you have two options. You can simply add です to ～ない. When you do this, you aren't actually saying "is" again. In this case, です's meaning is just showing politeness. Or, you can use ～｛では・じゃ｝ありません. If you remember from Lesson 8 that だ comes from である and that it will be important to know this later on, the time is now. Polite conjugations using it are "more polite" than just using です. So, they are best used with people whom you should show more respect."