I was asked to evaluate this integral where C is a straight line contour of $y=x$: $$\int_C\frac{1}{z^2+2i}dz$$
I keep getting stuck as the question did not provide any limits.
Is there any way of solving this or am I right in thinking that the question didn't provide me with enough information?
My guess would be that the contour is the entire straight line. That is, you would want to parameterize as \begin{equation} z = t + i t, \ \ \ \ \ \ t \in (-\infty,\infty) \end{equation} from here we can write \begin{equation} dz = (1 + i) dt, \ z^2 = 2 i t^2 \end{equation} and the contour integral becomes \begin{equation} \displaystyle \int_{-\infty}^{\infty} \frac{(1+i) dt}{2i (t^2 + 1)} = \frac{1}{2}(1-i) \displaystyle \int_{-\infty}^{\infty} \frac{ dt}{t^2 + 1} = \frac{\pi}{2}(1-i) \end{equation}