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Aus Online Mathematik Brückenkurs 2

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+iz−−1−i=z2+2z+2 

NOTE: If one wants to have all the polynomials which have only these zeros, the answer is

Cz+1−imz+1+in 

where C is a non-zero constant and m and n are positive integers.