Let the region R be defined by , if z is any point in the region R, and is its conjugate, find the corresponding region for w where

My solution was this. I know that and since the modulus of a complex number is a real number its square will be also. So we knowwis a real number and so will lie on the real line. In addition its modulus will be less than one, so I thinkwlies on the real axis between 0 and 1.

However the book says that it's any point inside the unit circle centered at the origin (i.e. no change). But wouldn't this be true for ?? The book definitely asks for , so is there a typo on the book or have I made a mistake?

Regards,

Stonehambey