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

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