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Cauchy’s integral formula for f(a) in polar form at any point a is:

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UPPCL AE Electrical 2 April 2022 Official Paper (Shift 2)
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  1.  f(reiθ)dθ
  2.  f(a + reiθ)dθ
  3. f(a + reiθ)dθ
  4. f(eiθ)dθ

Answer (Detailed Solution Below)

Option 3 : f(a + reiθ)dθ
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Detailed Solution

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Cauchy integral formula

If a complex function f(z) is analytic within and on a closed contour c inside a simply-connected domain, and if zo is any point in the middle of C, then the value of f(z) at z = zo is given by:

In polar form: 

(z = x + iy) is converted into (z = reiθ) form, where:

and 

 ​​​

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