1.10.16 Polynomials
condition: Find the values of the polynomial \( f(x) \) and its derivatives for \( x=x_{0} \) : \[ \begin{array}{l} f(x)=x^{4}-3 i x^{3}-4 x^{2}+5 i x-1 \\ x_{0}=1+2 i \end{array}\]
Polynomials and their complex, real and rational roots. Decomposition in various numerical fields.