find a Möbius transformation between the unit disc to $\{|\operatorname{im}(z)|<1\}$

Question

find a Möbius transformation between the unit disc to $\bigl\{|\operatorname{im}(z)|<1\bigr\}$ that satisfies: $f(0)=0,\; |f'(0|)>0$. My try: I tried to plug all this condition and got: $\frac{ax}{cx+d}$ and that a and d must have the same sign, but nothing else.