Determine four possible prime factorizations of 7+5i in Z[i]. Hint: To begin, factor the norm of 7+5i to guide your choices of primes m+ni so that (7+5i)/(m+ni) is also in Z[i]. Be sure to show all calculations needed to verify your results, including why your factors are primes in Z[i]. Give a factorization of 17 in Z[i] to verify that 17 is not prime in Z[i]. Then show why 11 can't be factored in Z[i].