- #1
abhijeet.26
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Homework Statement
determine the number of roots, counting multiplicities, of the equation z^7-5*z^3+12=0
in side the annulus 1<=|z|<2
Finding number of roots of a complex equation using rouche's theorem
- Thread starter abhijeet.26
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SUMMARY
The discussion focuses on determining the number of roots of the complex equation z7 - 5z3 + 12 = 0 within the annulus defined by 1 ≤ |z| < 2 using Rouché's theorem. Participants emphasize the importance of applying Rouché's theorem correctly to ascertain the number of roots by comparing the given function with a simpler function that dominates it in the specified region. The conversation highlights the need for a clear understanding of the theorem's application to complex analysis problems.
PREREQUISITES- Understanding of complex functions and their properties
- Familiarity with Rouché's theorem
- Knowledge of polynomial equations and their roots
- Basic concepts of annuli in the complex plane
- Study Rouché's theorem in detail, including examples and applications
- Explore complex analysis techniques for counting roots within specified regions
- Learn about the properties of polynomial functions in the complex plane
- Investigate other theorems related to root-finding in complex analysis
Students and educators in mathematics, particularly those focusing on complex analysis, as well as anyone interested in advanced techniques for solving polynomial equations in the complex plane.
determine the number of roots, counting multiplicities, of the equation z^7-5*z^3+12=0
in side the annulus 1<=|z|<2
- #2
tiny-tim
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Welcome to PF!
Hi abhijeet.26! Welcome to PF!
Show us what you've tried, and where you're stuck, and then we'll know how to help.
(and see http://en.wikipedia.org/wiki/Rouche's_theorem)
Hi abhijeet.26! Welcome to PF!
Show us what you've tried, and where you're stuck, and then we'll know how to help.
(and see http://en.wikipedia.org/wiki/Rouche's_theorem)
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