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The value of the integral
evaluated over a counter-clockwise circular contour in the complex plane enclosing only the pole z = i, where i is the imaginary unit, is
evaluated over a counter-clockwise circular contour in the complex plane enclosing only the pole z = i, where i is the imaginary unit, is
- a)(-1 + i) π
- b)(1 + i) π
- c)2(1 - i) π
- d)(2 + i) π
Correct answer is option 'A'. Can you explain this answer?
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Most Upvoted Answer
The value of the integralevaluated over a counter-clockwise circular c...
Concept:
Residue theorem: if f(z) is an analytic function in a closed curve C except at a finite number of singular points within C then
∮cf(z)dz = 2πi × (sum of the residues at the singular point within curve C)
Residue for simple pole z = a:
Res f(a) =
Calculation:
Residue theorem: if f(z) is an analytic function in a closed curve C except at a finite number of singular points within C then
∮cf(z)dz = 2πi × (sum of the residues at the singular point within curve C)
Residue for simple pole z = a:
Res f(a) =
Calculation:
Given:
pole z = i
Check for singularity at pole z = i
f(z) = 2z4 - 3z3 + 7z2 - 3z + 5
f(i) = 2(i)4 - 3(i)3 + 7(i)2 - 3i + 5
f(i) = 2 ×1 - 3(-i) - 7 - 3i + 5 = 0
since, f(i) = 0 ⇒ z = i is a singular point
From Residue theorem:
dz = 2πi (Residue at z = i )
dz = 2πi (Residue at z = i )
at z = i , Res = 0/0 form, applying L'hospital rule
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Community Answer
The value of the integralevaluated over a counter-clockwise circular c...
Concept:
Residue theorem: if f(z) is an analytic function in a closed curve C except at a finite number of singular points within C then
∮cf(z)dz = 2πi × (sum of the residues at the singular point within curve C)
Residue for simple pole z = a:
Res f(a) =
Calculation:
Residue theorem: if f(z) is an analytic function in a closed curve C except at a finite number of singular points within C then
∮cf(z)dz = 2πi × (sum of the residues at the singular point within curve C)
Residue for simple pole z = a:
Res f(a) =
Calculation:
Given:
pole z = i
Check for singularity at pole z = i
f(z) = 2z4 - 3z3 + 7z2 - 3z + 5
f(i) = 2(i)4 - 3(i)3 + 7(i)2 - 3i + 5
f(i) = 2 ×1 - 3(-i) - 7 - 3i + 5 = 0
since, f(i) = 0 ⇒ z = i is a singular point
From Residue theorem:
dz = 2πi (Residue at z = i )
dz = 2πi (Residue at z = i )at z = i , Res = 0/0 form, applying L'hospital rule
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The value of the integralevaluated over a counter-clockwise circular contour in the complex plane enclosing only the pole z = i, where i is the imaginary unit, isa)(-1 + i) πb)(1 + i) πc)2(1 - i) πd)(2 + i) πCorrect answer is option 'A'. Can you explain this answer?
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The value of the integralevaluated over a counter-clockwise circular contour in the complex plane enclosing only the pole z = i, where i is the imaginary unit, isa)(-1 + i) πb)(1 + i) πc)2(1 - i) πd)(2 + i) πCorrect answer is option 'A'. Can you explain this answer? for Civil Engineering (CE) 2024 is part of Civil Engineering (CE) preparation. The Question and answers have been prepared according to the Civil Engineering (CE) exam syllabus. Information about The value of the integralevaluated over a counter-clockwise circular contour in the complex plane enclosing only the pole z = i, where i is the imaginary unit, isa)(-1 + i) πb)(1 + i) πc)2(1 - i) πd)(2 + i) πCorrect answer is option 'A'. Can you explain this answer? covers all topics & solutions for Civil Engineering (CE) 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The value of the integralevaluated over a counter-clockwise circular contour in the complex plane enclosing only the pole z = i, where i is the imaginary unit, isa)(-1 + i) πb)(1 + i) πc)2(1 - i) πd)(2 + i) πCorrect answer is option 'A'. Can you explain this answer?.
The value of the integralevaluated over a counter-clockwise circular contour in the complex plane enclosing only the pole z = i, where i is the imaginary unit, isa)(-1 + i) πb)(1 + i) πc)2(1 - i) πd)(2 + i) πCorrect answer is option 'A'. Can you explain this answer? for Civil Engineering (CE) 2024 is part of Civil Engineering (CE) preparation. The Question and answers have been prepared according to the Civil Engineering (CE) exam syllabus. Information about The value of the integralevaluated over a counter-clockwise circular contour in the complex plane enclosing only the pole z = i, where i is the imaginary unit, isa)(-1 + i) πb)(1 + i) πc)2(1 - i) πd)(2 + i) πCorrect answer is option 'A'. Can you explain this answer? covers all topics & solutions for Civil Engineering (CE) 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The value of the integralevaluated over a counter-clockwise circular contour in the complex plane enclosing only the pole z = i, where i is the imaginary unit, isa)(-1 + i) πb)(1 + i) πc)2(1 - i) πd)(2 + i) πCorrect answer is option 'A'. Can you explain this answer?.
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