Hi, Im trying to find biholomorphic maps. More explicitly, let $\displaystyle D$ be the unit disk. Im looking for for biholomorphic maps that transform

a) the ellipse $\displaystyle E = \{z=x+iy | (x/a)^2 +(y/b)^2 < 1\}$

b) the half-strip $\displaystyle \{z \in \mathbb{C} | 0 < Re z < 1, Im z > 0\}$

into $\displaystyle D$. Any help for either a) or b) is appreciated.