Pooja posted an Question
July 13, 2021 • 10:36 am 30 points
  • CSIR NET
  • Mathematical Sciences

Please confirm the answr here singularity 1 lies on the boundary of region then can't we apply cauchy therorem??

z -z+1 Z-1 53. Evaluate dx, where C is the circle (A) when I2 = 1, 44tdz = 2mi Z 1 when z = 2-Z+ 1 z-1 Yon .'. =O (B -Z+ldz = 0 when z = 1, Jo z-1 4dz = 0 (C) z-2+ dz = 2ri (D) when zl z-1

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  • Alka gupta

    here ans must be A and B if circle |z|=1/2 then z=1 lies out side the circle so function is analytic inside C so by Cauchy integral theorem line integral is zero if circle |z|=1 then function is not analytic at boundary of circle so by residu theorm line integral = 2πi Res(z=1) ....2πi

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