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According to the factor theorem, a polynomial that has the zeros −1+i and −1−i must contain the factors z−(−1+i) and z−(−1−i). An example of such a polynomial is
(z−(−1+i))(z−(−1−i))=z2+2z+2.
Note: If one wants to have all the polynomials which have only these zeros, the answer is
C(z+1−i)m(z+1+i)n
where C is a non-zero constant and m and n are positive integers.
