MHB Complex Residue Calculation at a Specific Point

Click For Summary
The discussion centers on correcting the calculation of residues in complex analysis, specifically at the point z=3. The correct residue at this point is derived using the derivative of the function e^(iz) divided by the polynomial z^2 + 4z + 29. The calculated residue at z=3 is (5i-1)e^(3i)/250. Participants emphasize the importance of following proper steps to ensure accurate residue calculations. Accurate residue determination is crucial for complex function analysis and applications in various fields.
Doomknightx9
Messages
2
Reaction score
0
My residue is wrong. What is the solutions and the steps to achieve it ?
 

Attachments

  • d.JPG
    d.JPG
    16.6 KB · Views: 114
Physics news on Phys.org
Doomknightx9 said:
My residue is wrong. What is the solutions and the steps to achieve it ?
I think that you have the correct residues at $z = -2\pm5i$. The residue at $z=3$ is wrong. It should be $$\left.\frac d{dz}\,\frac{e^{iz}}{z^2 + 4z + 29}\right|_{z=3},$$ which I get to be $\dfrac{(5i-1)e^{3i}}{250}.$
 
Thread 'Problem with calculating projections of curl using rotation of contour'

Thread 'Problem with calculating projections of curl using rotation of contour'

Hello! I tried to calculate projections of curl using rotation of coordinate system but I encountered with following problem. Given: ##rot_xA=\frac{\partial A_z}{\partial y}-\frac{\partial A_y}{\partial z}=0## ##rot_yA=\frac{\partial A_x}{\partial z}-\frac{\partial A_z}{\partial x}=1## ##rot_zA=\frac{\partial A_y}{\partial x}-\frac{\partial A_x}{\partial y}=0## I rotated ##yz##-plane of this coordinate system by an angle ##45## degrees about ##x##-axis and used rotation matrix to...
View full post »

Similar threads

Insights An Overview of Complex Differentiation and Integration
  • · Replies 1 ·
Replies
1
Views
4K
A Cauchy’s integral theorem and residue theorem, what’s the difference
  • · Replies 1 ·
Replies
1
Views
2K
I Integrating a product of exponential and trigonometric functions
  • · Replies 21 ·
Replies
21
Views
3K
A A question about a complex integral
  • · Replies 8 ·
Replies
8
Views
3K
I Questions about the arg of complex numbers
  • · Replies 4 ·
Replies
4
Views
2K
Calculating Laurent series of complex functions
  • · Replies 3 ·
Replies
3
Views
1K
I Calculate the residue of 1/Cosh(pi.z) at z = i/2 (complex analysis)
  • · Replies 7 ·
Replies
7
Views
4K
Complex Integration Along Given Path
  • · Replies 3 ·
Replies
3
Views
2K
Complex analysis question: can't find similar question on internet
  • · Replies 2 ·
Replies
2
Views
3K
I Expansion of a complex function around branch point
  • · Replies 3 ·
Replies
3
Views
2K