Problem Set 2 Samuel
نویسنده
چکیده
Let f(z) = 1 z+2z+2 and note that on the real axis f corresponds to the integrand above. From the equation x2 + 2x + 2 = 0 and the quadratic formula, we find that the singularities of f are −1± i and both are clearly simple poles. Let R > √ 2, c1 : z = x (−R ≤ x ≤ R), and c2 : z = Re (0 ≤ θ ≤ π). Then c = c1+c2 is a simple closed contour that contains −1+i in its interior (see figure). By the Residue theorem,
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