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If $f(z) = c_{0} + c_{1} z^{-1},$ then $\oint_{\text{unit circle}} \frac{1+f(z)}{z} dz$ is given by

1. $2 \pi c_{1}$
2. $2 \pi\left(1+c_{0}\right)$
3. $2 \pi j c_{1}$
4. $2 \pi j\left(1+c_{0}\right)$