Math 412 Group Work #8 Spring 2009
Problem 1. Suppose that {zn}converges. Prove that {|zn|} converges. Is the
converse true?
Problem 2. Evaluate each limit when they exist:
(a): lim
nโโ
n3(1 + 3i)
2n3+ 4n+ 1.
(b): lim
nโโ ๎(โ1)n+(n+ 1)2i
n2+ 4 ๎.
(c): lim
nโโ hโn+ 1 โโn+ 2ii.
Problem 3. Suppose that {zn}converges. Show that {zn}is bounded in two ways:
(a): Use the corresponding fact that convergent sequences of real numbers are
bounded.
(b): Work it out directly from definitions.