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The value of the contour integral in the complex plane

along the contour |z| = 3, taken counterclockwise is
  • a)
    -18πi
  • b)
    0
  • c)
    14πi
  • d)
    48πi
Correct answer is option 'C'. Can you explain this answer?
Most Upvoted Answer
The value of the contour integral in the complex planealong the contou...
Concept:
For a given complex function with poles, the complex integralis given by
Residue theorem as;
C⁡f(z)dz = 2π i × {Sum of residue of poles in side or onC}
Calculation:

Contour: |z|= 3
Simple pole, z = 2 and it is lies inside the contour.
Residue of f(z) at z = 2 is,
= 23 − 2(2) + 3 = 7
f(z) = 2πi(7) = 14πi
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The value of the contour integral in the complex planealong the contour |z| = 3, taken counterclockwise isa)-18πib)0c)14πid)48πiCorrect answer is option 'C'. Can you explain this answer?
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