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Let $p\left ( z\right )=z^{3}+\left ( 1+j \right )z^{2}+\left ( 2+j \right )z+3$, where $z$ is a complex number.

Which one of the following is true?

  1. $\text{conjugate}\:\left \{ p\left ( z \right ) \right \}=p\left ( \text{conjugate} \left \{ z \right \} \right )$ for all $z$
  2. The sum of the roots of $p\left ( z \right )=0$ is a real number
  3. The complex roots of the equation  $p\left ( z \right )=0$ come in conjugate pairs
  4. All the roots cannot be real
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