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Let $S$ be the set of points in the complex plane corresponding to the unit circle. (That is, $S$={$z$ : $|z|$=$1$}). Consider the function $f(z)=zz^*$  where $z^*$ 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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