- #1
Complex Residue Calculation at a Specific Point
- Context: MHB
- Thread starter Doomknightx9
- Start date
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SUMMARY
The discussion centers on the calculation of complex residues, specifically addressing the residue at the point \( z = 3 \). The correct formula for calculating the residue is given as \( \left.\frac d{dz}\,\frac{e^{iz}}{z^2 + 4z + 29}\right|_{z=3} \), which evaluates to \( \dfrac{(5i-1)e^{3i}}{250} \). The residue at \( z = -2 \pm 5i \) is confirmed to be correct, while the residue at \( z = 3 \) was initially miscalculated. This highlights the importance of precise differentiation in residue calculations.
PREREQUISITES- Complex analysis fundamentals
- Understanding of residue theory
- Proficiency in differentiation of complex functions
- Familiarity with the exponential function in complex variables
- Study the application of the residue theorem in complex analysis
- Learn about differentiating complex functions using the Cauchy-Riemann equations
- Explore the properties of exponential functions in the context of complex variables
- Practice calculating residues at various poles in complex functions
Students and professionals in mathematics, particularly those specializing in complex analysis, as well as anyone involved in advanced calculus or mathematical physics requiring residue calculations.
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