4. Suppose that Ω ⊆ C \ {0} is a simply connected domain. Show that a branch of the log- arithm can be defined on Ω. (Hint: Use part (b) of Exercise 3 to define an antiderivative of f (z) = 1/z on Ω....

4. Suppose that Ω
⊆
C
\ {0}
is a simply connected domain. Show that a branch of the log- arithm can be defined on Ω. (Hint: Use part (b) of Exercise 3 to define an antiderivative of
f
(z) = 1/z
on Ω. Adjust by a constant, if necessary.) Compare with Exercise 21 in Section 2.4.