Technically, whenever you write anything, it is already copyright protected because you have physical proof that the content belongs to you. Your documents are date and time stamped. Once you publish your work, the book has a publication date. However, if you were to face a legal case for plagiarism in court, having the official paperwork to prove the exact date you’ve created your work would serve you better in the courthouse.
For peace of mind, I would suggest that you purchase an official copyright. It’s better to have one than to not.