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Let $S$ be the set of points in the complex plane corresponding to the unit circle. $(\text{That is}, S = \{z :\:\: \mid z \mid =1\}).$ Consider the function $f(z)=zz^{\ast}$  where $z^{\ast}$ denotes the complex conjugate of $z$. The $f(z)$ maps $S$ to which one of the following in the complex plane

  1. unit circle
  2. horizontal axis line segment from origin to $(1, 0)$
  3. the point $(1, 0)$
  4. the entire horizontal axis
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