This is probably a very simple questions but I am not clear on Möbius transformations and how to solve this problem. I'd appreciate if somebody can point me towards a method to do these sort of questions or a webpage that explains what I need to solve this problem.
On
When you use the word "isometry" you have to indicate the exact domain that should be mapped and the used metric(s) on the domain and codomain.
If you have just ${\mathbb C}$ with its euclidean metric in mind the simplest Möbius transformation mapping the point $i$ to $17+3i$ would be the translation $f:\ z\mapsto z+c$ with translation vector $c=17+2i$.
Consider $f(z)=3z+17$. It sends $i$ to $17+3i$ as desired and also preserves orientation since it is a polynomial over $z$ and hence a holomorphic function.
Edit: As "yoyo" already stated in the comments... I was being careless to see the comment.