The only singularity is a simple pole at z = −a, exactly at the circle’s centre. Its residue is 1. Every stated positive radius encloses this pole, and counterclockwise orientation gives integral $2\pi i$ by the residue theorem. Thus B, independently of a and R.
More Complex variables: Analytic functions, Cauchy's integral theorem and integral formula, Taylor's and Laurent's series, residue theorem, solution of integrals questions
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