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2. Let the function ƒ (²)=³-3z² + 2z 4-3z The poles of f(z) are z=0, 1 and 2 which are 3 simple poles. Given C:|z| = which represents a circle centered at 0 with a radius mia 4-3z c) By using the Cauchy's Residue Theorem, show that ₂³ -3z² + 2z dz = 2πi. 2 a) Determine the poles that lie within C. b) State the definition of residues. Hence, show that Res (fƒ,0) = 2 and Res(ƒ,1)=-1.

2. Let the function ƒ (²)=³-3z² + 2z 4-3z The poles of f(z) are z=0, 1 and 2 which are 3 simple poles. Given C:|z| = which represents a circle centered at 0 with a radius mia 4-3z c) By using the Cauchy's Residue Theorem, show that ₂³ -3z² + 2z dz = 2πi. 2 a) Determine the poles that lie within C. b) State the definition of residues. Hence, show that Res (fƒ,0) = 2 and Res(ƒ,1)=-1.

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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Please help me solve this Complex Analysis problems.

4-3z 2³-3z²+2z 2. Let the function f(z)=- 3 simple poles. Given C:|=|= which represents a circle centered at 0 with a radius The poles of f(z) are z = 0, 1 and 2 which are 3 4-3z c) By using the Cauchy's Residue Theorem, show that c ₂³ -32² + 2z dz = 2πi. N/W a) Determine the poles that lie within C. b) State the definition of residues. Hence, show that Res (ƒ,0) = 2 and Res(ƒ,1)=-1.
Transcribed Image Text:4-3z 2³-3z²+2z 2. Let the function f(z)=- 3 simple poles. Given C:|=|= which represents a circle centered at 0 with a radius The poles of f(z) are z = 0, 1 and 2 which are 3 4-3z c) By using the Cauchy's Residue Theorem, show that c ₂³ -32² + 2z dz = 2πi. N/W a) Determine the poles that lie within C. b) State the definition of residues. Hence, show that Res (ƒ,0) = 2 and Res(ƒ,1)=-1.
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