246 CHAPTER 6 • COMPLEX INTECRATION- EXAMPLE 6.27 Show that the function f (z) = sin z is not a bounded
function.
Solution We established this characteristic with a somewhat tedious argument
in Section 5.4. All we need do now is observe that f is entire and not constant,
and hence it is not bounded.
We can use Liouville's theorem to establish an important theorem of ele-
mentary algebra.