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I integrated $f(z) = z$ conjugate on two different line segments

a) from $0$ to 1 then to $1 + i$ b) from $0$ to $1 + i$ directly

And I correctly obtained answers of $1 + i$ for a) and $1$ for b)

but why are the answers different

Elli
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  • Are there any underlying principle that you expect complex integral shall obey? – Ken Hung May 27 '21 at 04:25
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    Do you realize that we don't have path independence for line integrals of real-valued functions either? – saulspatz May 27 '21 at 04:30
  • Well, what reason is there to expect them to be the same? You're effectively integrating two totally different functions, one of which is given by the values of $f$ on one path and one if which is given by the values of $f$ on another path. – Eric Wofsey May 27 '21 at 04:35

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