Can I copy my own work within the same class?
There are two issues to consider, self-plagiarism and meeting the course requirements.

The existing answer deals effectively with the self-plagiarism issue. If you quote and attribute just as you would for something written by someone else, you are not plagiarizing.

Even so, your paper might get a poor grade for not meeting course requirements. It would be unusual to set two exercises such that quoting the first one is sufficient for the second. For example, you may be expected to go into more depth.

Consulting the professor is the best solution to that issue.