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Suppose $x_{1}(t)$ and $x_{2}(t)$ have the Fourier transforms as shown below.

Which one of the following statements is TRUE?

  1. $x_{1}(t)$ and $x_{2}(t)$ are complex and $x_{1}(t) x_{2}(t)$is also complex with nonzero imaginary part
  2. $x_{1}(t)$ and $x_{2}(t)$ are real and $x_{1}(t) x_{2}(t)$is also real
  3. $x_{1}(t)$ and $x_{2}(t)$ are complex but $x_{1}(t) x_{2}(t)$ is real
  4. $x_{1}(t)$ and $x_{2}(t)$ are imaginary but $x_{1}(t) x_{2}(t)$ is real
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