2. Let a ∈ C and r > 0. Suppose that f, g ∈ H(A(a; 0, r)) have poles of orders n and m, respectively, at a. (a) What can be said about the singularity of f + g at a? Give examples. (b) What can be...

2. Let
a

∈
C and
r


>
0. Suppose that
f,


g

∈

H(A(a; 0,

r)) have poles of orders
n
and
m, respectively, at
a.

(a) What can be said about the singularity of
f
+
g
at
a? Give examples.

(b) What can be said about the singularity of
fg
at
a? Give examples.