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gabbagabbahey said:The complex Residues method should work fine; why don't you show us what you tried for that method...
gabbagabbahey said:I won't be able to read your attempt until admin approves your attachment. You can save time by uploading your file to imageshack.us and posting a link to it instead.
gabbagabbahey said:To make your calculations easier, you should note that if [itex]|z^2|>1[/itex] then so is [itex]|z|[/itex]; and [itex]3+2\sqrt{2}>1[/itex].
Also note that [tex]\sqrt{3-2\sqrt{2}}=\sqrt{2}-1[/tex]
asi123 said:I've to warn you, The numbers are awful.
gabbagabbahey said:They sure are!
Luckily, they're also correct...you can simplify them though...after a little algebra you should find that [itex]A=B=\frac{-1}{\sqrt{2}}[/itex] and so your final result becomes [itex]2\pi(\sqrt{2}-1)[/itex]
Complex Analysis is a branch of mathematics that deals with the study of complex numbers and their properties. It involves the analysis of functions that are defined on the complex plane and the use of techniques such as differentiation, integration, and power series to understand their behavior.
Some common topics covered in a Complex Analysis course include complex numbers, complex functions, analytic functions, Cauchy-Riemann equations, contour integration, power series, residues, and conformal mapping.
Complex Analysis has a wide range of applications in various fields such as physics, engineering, economics, and computer science. Some specific applications include electromagnetism, fluid dynamics, signal processing, and computational methods.
One of the main challenges students face in understanding Complex Analysis is the abstract nature of the subject. It involves concepts and techniques that are not typically encountered in other branches of mathematics. The use of complex numbers and the geometric interpretation of functions can also be challenging for some students.
To improve your understanding of Complex Analysis, it is important to have a strong foundation in calculus, especially in the topics of limits, derivatives, and integrals. It is also helpful to practice solving problems and to seek help from tutors or professors when needed. Additionally, visual aids such as diagrams and animations can be useful in understanding complex concepts.