1. The problem statement, all variables and given/known data Determine whether the sequence zn = n/((1+i)n) converges and rigorously justify your answer. 2. Relevant equations 3. The attempt at a solution I have attempted an ε-n proof using my limit as 0 (as exponentials grow faster than polynomials I assumed this was the correct limit), and I said |(1+i)n| = |1+i|n = √2 n but I was stuck with how to show n/(√2 n) < ε. The only other way I could think to do this was to show the sequence was increasing (or decreasing) and bounded above (or below) but I wasn't sure how to do that either. Can someone please point me in the right direct? I find complex sequences quite confusing as a concept.