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- Homework Statement
- I am asked to find the value of the integral I = dz / (z * (z + 4)) along the contour z = 4 * t * exp(-t * 2* pi * i) + 1, where the bounds of t are [0,1].

- Relevant Equations
- Cauchy's Integral Formula, Residue Theorem

From plotting the given path I know that the path is a curve that extends from z = 1 to z=5 on the complex plane. My plan was to parametrize the distance from z = 1 to 5 as z = x, and create a closed contour that encloses z=0, where I could use Cauchy's Integral Formula, with f(z) being 1 / (z + 4). This gives me an answer of I = 2 * pi * i, but I know the answer is supposed to be 0.255 (from evaluating the integral directly between z=1 and z=5. Using the Residue Theorem gives me the same answer, so I am unsure of how to proceed,