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By Cauchy's Theorem, it is easy to see that the integral of cos z in the square contour determined by corners 0, 1, 1+i, i,

By Cauchy's Theorem, it is easy to see that the integral of cos z in the square contour determined by corners 0, 1, 1+i, i, is zero. Can you prove this by calculating the integral in each of the four sides of the contour?

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