7.4 • SINGULARITIES, ZEROS, AND POLES 281Corollaries 7.5- 7.8 are useful in determining the order of a zero or a pole.
The proofs follow easily from Theorems 7.10 and 7.12, and are left as exercises.
II Corollary 7 .5 If f is analytic and has a zero of order k at the point a, then
g (z) = yf.J has a pole of order k at a. •