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Let (-1 - j), (3 - j), (3 + j) and (-1 + j) be the vertices of a rectangle C in the complex plane. Assuming that C is traversed in counter-clockwise direction, the value of the countour integral  is
  • a)
    0
  • b)
    jπ/16
  • c)
    jπ/2
  • d)
    -jπ/8
Correct answer is option 'D'. Can you explain this answer?
Most Upvoted Answer
Let (-1 - j), (3 - j), (3 + j) and (-1 + j) be the vertices of a recta...
Concept:
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

2. If f(z) has a pole of order n at z = a, then

Application:
Given (-1 - j), (3 - j), (3 + j) and (-1 + j) are the vertices of a rectangle C in the complex plane

f(z) from the given data is,

 
Poleas of f(z) is
z = 0 of order n = 2, lies in side the closed curve.
z = 4 of order n = 1, lies outside the closed curve.
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Community Answer
Let (-1 - j), (3 - j), (3 + j) and (-1 + j) be the vertices of a recta...
Concept:
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

2. If f(z) has a pole of order n at z = a, then

Application:
Given (-1 - j), (3 - j), (3 + j) and (-1 + j) are the vertices of a rectangle C in the complex plane

f(z) from the given data is,

 
Poleas of f(z) is
z = 0 of order n = 2, lies in side the closed curve.
z = 4 of order n = 1, lies outside the closed curve.
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Let (-1 - j), (3 - j), (3 + j) and (-1 + j) be the vertices of a rectangle C in the complex plane. Assuming that C is traversed in counter-clockwise direction, the value of the countour integralisa)0b)jπ/16c)jπ/2d)-jπ/8Correct answer is option 'D'. Can you explain this answer?
Question Description
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