Find the limit of complex number

Question

I have $$Z_n = e^{-i({\frac{\pi}{2}+{\frac{1}{2n}}})}$$ Therefore, as $n \to \infty$, $$\operatorname{\lim}Z_n = e^{-i{\frac{\pi}{2}}}$$ But the answer on the book is $i.$

Answer 1

Note that $$e^{-i\pi /2} = \cos (-\pi/2) -i \sin(\pi/2)=-i$$

Thus the book has a typo.