OP's equation 1.7 suggests something to me that wasn't highlighted.
Centered at the origin in R2, I expected inverse of r times e^iTheta to be be 1/r times e^-iTheta. Their product is then 1. I believe that is in equation 1.7 .
For that apparently special case, points on a larger-than-unit circle map to points on a smaller-than-unit circle.
OP's equation 1.7 suggests something to me that wasn't highlighted.
Centered at the origin in R2, I expected inverse of r times e^iTheta to be be 1/r times e^-iTheta. Their product is then 1. I believe that is in equation 1.7 .
For that apparently special case, points on a larger-than-unit circle map to points on a smaller-than-unit circle.