If you are interested in conformal mapping you can read the entire detailed thread here.
Let , let , let , let , let . Thus, is translation, is inversion, is rotation (by ), is dilation, and is translation.
However, .
I don't know how to approach the following problem : Write the transformation as a composition of translations, rotations, dilatations and inversions. Use the result to find the image of the semi-plane .
My attempt : My idea was to write in the form but I didn't reach anything important I believe.
So I guess there's a better way to approach the problem. I'd like to know it/them.
Thanks a lot TPH! (I'll take some time to read through the link... seems really interesting. I don't know if my course will introduce me conformal mapping, it is made for physicists.)
Just a little question... why did you bother to rewrite in the form ?
I see that you got rid of a z over z form... is it a general way to solve problem like these?