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.