This is a question in an online complex analysis course I am taking, but I can't seem to get the right answer, the furtherest I've gotten is

$$\frac{e^{\frac{\pi }{2}+i\pi }+e^{-i\left(\frac{\pi }{2}+i\pi \right)}}{2},$$

can't figure out a solution, would be grateful for any help ( as you can see, I love math, but it is not mutuial).