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The closed loop line integral 
evaluated counter-clockwise, is
evaluated counter-clockwise, is- a)+8jπ
- b)-8jπ
- c)-4jπ
- d)+4jπ
Correct answer is option 'A'. Can you explain this answer?
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Most Upvoted Answer
The closed loop line integralevaluated counter-clockwise, isa)+8jπb...
Concept:
Residue Theorem:
If f(z) is analytic in a closed curve C except at a finite number of singular points within C, then
Residue Theorem:
If f(z) is analytic in a closed curve C except at a finite number of singular points within C, then
∫cf(z) dz = 2πj × [sum of residues at the singular points within C]
Formula to find residue:
1. If f(z) has a simple pole at z = a, then
Resf(α) = 
a[(z−α)f(z)]
a[(z−α)f(z)]2. If f(z) has a pole of order n at z = a, then
Calculation:
z + 2 = 0 z = -2 |z| = 2 < 5
f(x) is not analytic at z = -2
By Cauchy’s residue theorem
f(x) dz = 2πi × (sum of residues)At z = -2
Residue of f(x) = 
= -8 + 4 + 8 = 4
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Community Answer
The closed loop line integralevaluated counter-clockwise, isa)+8jπb...
Concept:
Residue Theorem:
If f(z) is analytic in a closed curve C except at a finite number of singular points within C, then
Residue Theorem:
If f(z) is analytic in a closed curve C except at a finite number of singular points within C, then
∫cf(z) dz = 2πj × [sum of residues at the singular points within C]
Formula to find residue:
1. If f(z) has a simple pole at z = a, then
Resf(α) = a[(z−α)f(z)]
a[(z−α)f(z)]2. If f(z) has a pole of order n at z = a, then
Calculation:
z + 2 = 0 z = -2 |z| = 2 < 5
f(x) is not analytic at z = -2
By Cauchy’s residue theorem
f(x) dz = 2πi × (sum of residues)At z = -2
Residue of f(x) =
= -8 + 4 + 8 = 4
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The closed loop line integralevaluated counter-clockwise, isa)+8jπb)-8jπc)-4jπd)+4jπCorrect answer is option 'A'. Can you explain this answer?
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