Complex Analysis: Confirmation for a question in my textbook? I'm being told that $$\frac{\exp{(1+i3\pi})}{\exp{(-1+i\pi /2})}= \exp(2)i$$
I keep getting $-\exp(2)i$. I have no idea how they didn't get that to be negative.

Relatively straightforward :
$$\frac{\exp{(1+i3\pi})}{\exp{(-1+i\pi /2})}= \frac{e \exp({i3\pi})}{e^{-1}\exp{(i\frac{\pi}{2}})} =  \frac{e\times(-1) }{e^{-1}\times i} = -e^2 \frac{1}{i}$$
But $\frac{1}{i} = -i$ (because $-1 = i\times i$ then you divide by $i$) so you get 
$$\frac{\exp{(1+i3\pi})}{\exp{(-1+i\pi /2})}=ie^2$$
