Prove that |z|^n ---> 0 if |z| < 0 1. The problem statement, all variables and given/known data This isn't really a homework problem; I'm preparing for an upcoming course and trying to recall how to do these basic proofs. 2. Relevant equations Definition of convergence 3. The attempt at a solution We seek a positive integer N such that for any positive number ∂, | |z|n - 0 | < ∂ whenever n ≥ N. Fix ∂ > 0. | |z|n- 0| = |z|n < ∂ iff n < log(∂) / log(|z|) (some steps omitted) But here's the problem: I have n smaller than a positive number, since log(∂), log(|z|) < 0 when ∂, |z| < 1. What do?