According to the Remark, since f(z) = 1/z is its own inverse function, the mapping w = 1/z...

According to the Remark, since f(z) = 1/z is its own inverse function, the mapping w = 1/z on the extended complex plane maps the circle  to the line Re(w) = 1. Verify this fact directly using the real and imaginary parts of f as in Example.

Example Image of a Semicircle under w = 1/z

FIGURE 2.5.4

Remarks