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# Complex Variables 115: Bonus Question.

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All steps must be shown, even small details. Workout the relevant calculations please complete the problem, not just set it up. Provide common sense explanations.

Bonus: The function p(z)=[z(z+1)]^-1 can be written in two different ways:

(see attached for full equation)

These two expansions are contradictory. The first seems to indicate that p(z) has a simple pole at z=0 and the residue is zero. Can you resolve this apparent contradiction? Which statement is correct? (Hint: Try to determine the region in which each expression is valid.)

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The expansions use the formula for summation of an infinite geometric ...

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