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I've got the next problem in complex analysis: find the bilinear transformation from A to B:

$${A = [z: \text{Re } z \ge-1 ]},\quad B = [w: |w|\ge1]$$

first, I tried to determine what each of the domains looks like. As I understand it (please correct me if not), the plot of domain $A$ is all the area satisfies $x\ge-1$ (and all the y's included). The plot of domain $B$ is a closed ring with a radius of $1$, and the area covered is everything outside the circle. Tried to take $3$ points of each boundary and plug it into the next formula: The formula

the problem is I'm getting a weird solution which does not satisfy the conditions. thanks.

Sebastiano
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Phisagi
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  • try this $z \mapsto \frac{z+3}{z-1}$, similar post https://math.stackexchange.com/questions/114733/mapping-half-plane-to-unit-disk – 138 Aspen Jan 04 '23 at 14:55
  • @138Aspen But how you figured it? did you take boundary points, or its something I'm missing from movius transformation?

    edit: checked the post, I think I understood this way. however, I'm trying now to understand what I did wrong my checking 3 points from the plane

     – Phisagi Jan 04 '23 at 16:12

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