Let .
What's the image of :
1)A circle with radius centered at ?
2)A circular semi-ring , , ?
What's the preimage by of the semi-plane ?
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For now I'm only looking for help for the 1).
My attempt : I wrote as to get . I don't recognize what it is. Especially the part .
Any idea about how I could rewrite ?
How strange. By the way I never learned about Mobius transformations yet but I know I will in less than a month I guess.
How would I find the inverse function? I'm thinking about finding a matrix and finding the inverse of it... but I'm unsure. I'd like to know how you would do it. (without posting the full solution )Originally Posted by TPH
Ah ok! Thanks for the correction.
It seemed strange to me because would send circles to exactly the same circles, but if you add the term, it shouldn't be circles anymore.
A circle is mapped to the same circle plus the inverse of this circle.
I don't know what is this "inverse of this circle".