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**Stonehambey** Let the region R be defined by $\displaystyle |z|<1$, if z is any point in the region R, and $\displaystyle z^*$ is its conjugate, find the corresponding region for w where $\displaystyle w=zz^*$

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 $\displaystyle |w|=zz^*$?? The book definitely asks for $\displaystyle w=zz^*$, so is there a typo on the book or have I made a mistake?