Find a Möbius transformation $g$ such that $f(z) = g(z)$ for all $z \in D$.

Question

Let $f$ be a function with domain $D= ${$z \in \mathbb C$: $|z| < 8$} given by $$ f(z) =\sum_{n≥0}\dfrac{i^nz^n}{8^n}. $$

Find a Möbius transformation $g$ such that $f(z)=g(z)$ for all $z \in D$. Calculate $f(i)$ and $f'(0)$.