I'm integrating 1/(z-1/2) over the closed disk w/ radius = 3 centered at 0. I've seen other problems where the final answer was i2pi times f(w) - here w =1/2. Since f(z) is equal to 1. Is the final answer just i2pi? Next up: I have the integral of dt/(2 + sint) the problem then tells me expand sin to its complex definition and replace e^it with z. My question is what does dt become? Lastly: I'm given the integral zexp(z^2). I'm asked to provide a proof for why it equals zero on any closed curve gamma. Do I simply perform a u sub (u=z^2, du=2zdz) and then say that since e^u is entire and thus holomorphic on any region (or curve) it is equal to 0?