Let $f(x)=x^4-6 x^3+26 x^2-46 x+65$. All roots of $\mathrm{f}(\mathrm{x})=0$ are of the form $a_k+i

Question

Let $f(x)=x^4-6 x^3+26 x^2-46 x+65$. All roots of $\mathrm{f}(\mathrm{x})=0$ are of the form $a_k+i b_k$ for $\mathrm{k}=1,2,3,4$ where $i=\sqrt{-1}$ further $a_k, b_k \in z$ (Set of integers) also $\lambda=\left|b_1ight|+\left|b_2ight|+\left|b_3ight|+\left|b_4ight|$ and $\mu=a_1+a_2+a_3+a_4$ and $S$ is a set containing all ai's, bi's.\

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