Can someone evaluate this? I'm having trouble as I could not get that answer
I get $$-i(\frac{z(z^{44}-1)}{z-1} - \frac{z^{-1}(z^{44}-1)}{z^{-1}-1}) + 1 $$
$$-i(z^{44}-1)\frac{z+1}{z-1} +1$$
since $z=cis(2)$ then $z^{45} = i$ and $z^{44} = \frac{i}{z}$
then I get $$\frac{iz^2+iz+1+z^2}{z^2-z}$$
Can someone spot the mistake??