What is the difference between following approaches concerning line integrals:
first approach is for complex function with parametrization $\gamma(t) = \cos t+i\sin t$ (Line_integral :: Example from Wikipedia).
Second approach is for $f(x,y)$ with parametrization $x=\cos t, y=\sin t$ (Line_integral :: Example from khanacademy.org).
Yes complex function $f(z)=1/z$ is $f: C \rightarrow C$ while the other is $f:R^2 \rightarrow R$, but what other differences there are or are they same thing said in different method?