Residue at poles of complex function

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Homework Help Overview

The discussion revolves around finding residues at poles of a complex function using the residue theorem. Participants are examining the steps involved in identifying poles and applying the theorem correctly.

Discussion Character

  • Exploratory, Assumption checking, Problem interpretation

Approaches and Questions Raised

  • Participants express confusion regarding the cancellation of terms in the numerator and the correct factors to use when differentiating. There are attempts to clarify the residue calculation at specific poles.

Discussion Status

Some participants are questioning the correctness of their approaches and the book's answer, while others are providing clarifications about the differentiation process and the factors involved. There is an ongoing exploration of different interpretations of the problem.

Contextual Notes

There is mention of specific terms and factors that may lead to confusion, such as the cancellation of certain expressions during the residue calculation. The discussion reflects a lack of consensus on the correct approach to the problem.

jaus tail
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Homework Statement


upload_2018-2-2_11-34-2.png


Homework Equations


First find poles and then use residue theorem.

The Attempt at a Solution


upload_2018-2-2_11-33-42.png

Book answer is A. But there's no way I'm getting A. The 81 in numerator doesn't cancel off.
 

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jaus tail said:

Homework Statement


View attachment 219529

Homework Equations


First find poles and then use residue theorem.

The Attempt at a Solution


View attachment 219528
Book answer is A. But there's no way I'm getting A. The 81 in numerator doesn't cancel off.

Be careful. You don't multiply the function by ##(3z+2)^3## before you differentiate it. What's the correct factor? You won't get the books answer A in any case, but that's the books problem.
 
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I don't get your answer or any of the answers above. It's hard for me to read your writing.
 
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Dick said:
Be careful. You don't multiply the function by ##(3z+2)^3## before you differentiate it. What's the correct factor? You won't get the books answer A in any case, but that's the books problem.
The (3z+2)3 will get canceled when I find residue at z = -2/3, just like the (3z-2)3 part will get canceled when I find residue at z = 2/3.
 
jaus tail said:
The (3z+2)3 will get canceled when I find residue at z = -2/3, just like the (3z-2)3 part will get canceled when I find residue at z = 2/3.

The residue formula has ##(z-a)^3## where ##a=(-2/3)##. That's not ##(3z+2)^3##.
 
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upload_2018-2-2_20-44-35.png

Yeah you're right. In solved example they've broken 0.5z - 1.5i to z - 3j and multiplied 2 into numerator. Thanks.
 

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