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Question 2. Use partial fraction to express the following as a sum of two terms of the form 201±i i.e. (1) 1 1 A 2² + 2x + 2 (z - (−1+i))(z-(-1 - i)) z- (-1 + i) (2) Use this expression to evaluate the following integral over the circle T:= = {z- i 2} using the Cauchy integral theorem; = √₁2² +²2² +2 d² S dz. 22 + z B (-1-i) 2-20¹ where

Question 2. Use partial fraction to express the following as a sum of two terms of the form 201±i i.e. (1) 1 1 A 2² + 2x + 2 (z - (−1+i))(z-(-1 - i)) z- (-1 + i) (2) Use this expression to evaluate the following integral over the circle T:= = {z- i 2} using the Cauchy integral theorem; = √₁2² +²2² +2 d² S dz. 22 + z B (-1-i) 2-20¹ where

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Question 2. Use partial fraction to express the following as a sum of two terms of the form 20-1ii.e. (1) = 1 1 A z²+2x+ 2 (z − (−1 + i)) (z − (−1 − i)) z − (−1 + i) (2) Use this expression to evaluate the following integral over the circle T := {|z − i = 2} using the Cauchy integral theorem; √xz²+25+2ds. + B z − (− 1 – i) * 1 2-20' where
Transcribed Image Text:Question 2. Use partial fraction to express the following as a sum of two terms of the form 20-1ii.e. (1) = 1 1 A z²+2x+ 2 (z − (−1 + i)) (z − (−1 − i)) z − (−1 + i) (2) Use this expression to evaluate the following integral over the circle T := {|z − i = 2} using the Cauchy integral theorem; √xz²+25+2ds. + B z − (− 1 – i) * 1 2-20' where
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