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Let C represent the unit circle centered at origin in the complex plane, and complex variable, z = x + iy. The value of the contour integral (where integration is taken counter clockwise) is
  • a)
    2πi
  • b)
    πi
  • c)
    0
  • d)
    2
Correct answer is option 'B'. Can you explain this answer?
Verified Answer
Let C represent the unit circle centered at origin in the complex plan...
Concept:
Cauchy's Integral Formula:
For Simple Pole:
If f(z) is analytic within and on a closed curve c and if a (simple pole) is any point within c, then

Calculation:
Given:
where C represents unit circle i.e. radius is unity.
The above equation can be written in standard form i.e. 
Therefore f(z) = and a = 0.
The pole of the given function is at z = 0, and lie inside the circle.

Cauchy's Integral Formula:
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Most Upvoted Answer
Let C represent the unit circle centered at origin in the complex plan...
Concept:
Cauchy's Integral Formula:
For Simple Pole:
If f(z) is analytic within and on a closed curve c and if a (simple pole) is any point within c, then

Calculation:
Given:
where C represents unit circle i.e. radius is unity.
The above equation can be written in standard form i.e. 
Therefore f(z) = and a = 0.
The pole of the given function is at z = 0, and lie inside the circle.

Cauchy's Integral Formula:
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Let C represent the unit circle centered at origin in the complex plane, and complex variable, z = x + iy. The value of the contour integral(where integration is taken counter clockwise) isa)2πib)πic)0d)2Correct answer is option 'B'. Can you explain this answer?
Question Description
Let C represent the unit circle centered at origin in the complex plane, and complex variable, z = x + iy. The value of the contour integral(where integration is taken counter clockwise) isa)2πib)πic)0d)2Correct answer is option 'B'. 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 Let C represent the unit circle centered at origin in the complex plane, and complex variable, z = x + iy. The value of the contour integral(where integration is taken counter clockwise) isa)2πib)πic)0d)2Correct answer is option 'B'. 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 Let C represent the unit circle centered at origin in the complex plane, and complex variable, z = x + iy. The value of the contour integral(where integration is taken counter clockwise) isa)2πib)πic)0d)2Correct answer is option 'B'. Can you explain this answer?.
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