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.