It is a smart form of insurance to keep scans of handwritten homework assignments. I do this with all valuable handwritten notes. If you do not know how to scan a document to PDF, ask the Undergraduate (or Graduate) Office for ideas. Be careful to set the scanner resolution at a reasonable level so that the resulting file is not too enormous (UTmail+ will refuse an attachment above 50MB).
I recommend that every serious student of physics owns a copy of Mathematica or Maple. However, these apps cost serious money, and in order to make a more level playing field I am going to recommend that everyone uses the less capable but entirely free open source Maxima. Learning how to program a symbolic algebra engine like Maxima will help you check laborious hand computations for homework assignments. You will still be required to show all of the steps in your working for each problem, but the computer should help you avoid getting physically misdirected by simple algebraic mistakes in your hand calculations.