Residue at poles of complex function

Click For Summary
The discussion centers around finding residues at the poles of a complex function using the residue theorem. Participants express confusion over the correct application of the theorem, particularly regarding the cancellation of factors in the numerator. There is a specific mention of the factor (3z+2)^3 and its role in calculating residues at z = -2/3 and z = 2/3. The conversation highlights discrepancies between personal calculations and the book's answer, emphasizing the need for careful differentiation and factor handling. Overall, the thread illustrates the complexities involved in applying the residue theorem correctly.
jaus tail
Messages
613
Reaction score
48

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.
 

Attachments

  • upload_2018-2-2_11-33-42.png
    upload_2018-2-2_11-33-42.png
    42.5 KB · Views: 824
  • upload_2018-2-2_11-34-2.png
    upload_2018-2-2_11-34-2.png
    2.8 KB · Views: 806
Physics news on Phys.org
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.
 
  • Like
Likes FactChecker and jaus tail
I don't get your answer or any of the answers above. It's hard for me to read your writing.
 
  • Like
Likes jaus tail
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##.
 
  • Like
Likes jaus tail
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.
 

Attachments

  • upload_2018-2-2_20-44-35.png
    upload_2018-2-2_20-44-35.png
    50.4 KB · Views: 417

Thread 'Distance between a Clock's hands when the distance is increasing most rapidly'

Question: A clock's minute hand has length 4 and its hour hand has length 3. What is the distance between the tips at the moment when it is increasing most rapidly?(Putnam Exam Question) Answer: Making assumption that both the hands moves at constant angular velocities, the answer is ## \sqrt{7} .## But don't you think this assumption is somewhat doubtful and wrong?
View full post »

Similar threads

Calculating Integral Using Residue Theorem & Complex Variables
  • · Replies 4 ·
Replies
4
Views
2K
Residue Theorem: Finding the Integral of z^3e^(-1/z^2) over |z|=5
  • · Replies 6 ·
Replies
6
Views
2K
How to find the residue of a complex function
  • · Replies 14 ·
Replies
14
Views
3K
Calculating Laurent series of complex functions
  • · Replies 3 ·
Replies
3
Views
1K
Contour integration around a complex pole
  • · Replies 2 ·
Replies
2
Views
3K
Find the residues of the following function + Cauchy Residue
  • · Replies 2 ·
Replies
2
Views
1K
Contour integral using residue theorem
  • · Replies 4 ·
Replies
4
Views
3K
What are the orders of the poles and the residue for sin(1/z)/cos(z)?
  • · Replies 3 ·
Replies
3
Views
3K
Complex Integration Along Given Path
  • · Replies 3 ·
Replies
3
Views
2K
Compute the residue of a function
  • · Replies 2 ·
Replies
2
Views
2K