Contour integral $\int_{0}^{\infty}\frac{e^{iz}}{(z-i)^2} \, \mathrm{d}z$

Question

$$\int_{0}^{\infty}\frac{e^{iz}}{(z-i)^2} \, \mathrm{d}z$$

I am unsure of what contour to use to evaluate this integral. I have done such integrals bounded from -infinity to infinity. Should I substitute cosz for the e^iz and use the fact that it’s an even function so that I can somehow half my result?

Answer 1

I tried this. Does this seem like the right idea?