I am trying to find the integral
$\oint_c Re(z)\;dz$ where c is a circle $|z|=2$
I don't know what to do.
I tried some things but I don't know if I am correct. $e^{i\theta} = \cos \theta +i \sin \theta$, so $Re(z) = \cos \theta$? And then $\int_0^{2\pi} 2\cos \theta i e^{i\theta}\;d\theta$
Can someone explain a little what's going on cause I am trying to understand it 2 hours now and I am getting nervous.