Unformatted text preview: n ≥ 1 at z . Prove that f /f has a simple pole at z . Exercise 3. Find all the singularities of f ( z ) = ( z-2) 2 ( z + 4) 1-cos( πz ) and identify each as removable, a pole of a certain order, or an essential singularity. Exercise 4. Repeat the preceding exercise for f ( z ) = ( z-2 i ) 4 sin( πi/z )-1 ....
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- Fall '11