Suppose we have an analytic function then Why complex integral of that function does not depend on the path of integration?
2026-03-25 12:30:07.1774441807
Complex line integrals
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In general, the complex integral depends on the path of integration !
Example: $D= \mathbb C \setminus \{0\}, f(z)=1/z$ and $c(t)=e^{it}$ with $t \in [0, 2m \pi i]$ for some $m \in \mathbb N$.
Then we have $\int_c f(z) dz = 2m \pi i$.