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let C be the contour described by |z| = 2 (the circle of radius 2). g has poles at z1 and z2. The moduli of these points are less than 2 and thus lie inside the contour. This integral can be split into two smaller integrals by Cauchy–Goursat theorem; that is, we can express the integral around the contour as the sum of the integral around z1 and z2 where the contour is a small circle around each pole. Call these contours C1 around z1 and C2 around z2. Now, each of these smaller integrals can be evaluated by the Cauchy integral formula
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