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Let $\mathbb{D} \subset \mathbb{C}$ be the unit disk. Let $\mathfrak{H}$ denote the right half-plane and let $\displaystyle f(z) = \frac{2z^2}{(1+z)^{2}}$. What is the image of $\mathfrak{H}$ under the map $f$?

A brief solution would help.

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