Julian Homework 2

COMMENTS:

12.1. Hah, too easy.

12.2. Good catch, squaring does not guarentee real. For future reference, multiplying by the complex conjugate guarentees the number becomes real. b: Good, ok to use informal word real, just make sure you do not do this in school. c) good, except it should be Z, not R in the last sentence.

12.7. Exactly!

11.3 Great! See, we still got number theory.

11.4. Good use of corollary 1.3.

11.12. BEAUTIFUL! WHOA! Even I had to work on this one for a while before I got it. And most people did not get it. But dude, I never taught you Cauchy's theorem. Did you read ahead or did you look this proof up (I would not blame you because the proof is HIGHLY non-trivial). If it is original, WHOA. Little error is that you forgot to argue why there is no smaller order than lcm(p_1,...), but that arguement is simple since it would contradict an individual element's definition of order being least. INCREDIBLY good job. This may be the hardest/most constructive solution you have derived. Beautiful. Simply beautiful.