Aus Online Mathematik Brückenkurs 2

According to the factor theorem, a polynomial that has the zeros \displaystyle -1+i and \displaystyle -1-i must contain the factors \displaystyle z-(-1+i) and \displaystyle z-(-1-i). An example of such a polynomial is

\displaystyle (z-(-1+i))(z-(-1-i)) = z^2+2z+2\,\textrm{.}

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

\displaystyle C(z+1-i)^m(z+1+i)^n

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