## conformal map, upper half-plane

Find a conformal map $w(z)$ of the right half-disk $\{ \text{Re}(z), |z|<1 \}$ onto the upper half-plane that maps $-i$ to $0$, $+i$ to $\infty$, and $0$ to $-1$. What is $w(1)$?

The back of the book says that $w=\frac{-(z+i)^2}{(z-i)^2}$, $w(1)=1$. However, I still do not see how they get $w=\frac{-(z+i)^2}{(z-i)^2}$. For the second part we can plug in $1$ to get $1$ as the output. I just don't see how to get $w=\frac{-(z+i)^2}{(z-i)^2}$. Thanks in advance.