Complex Eigenvalues

Algebra Level 5

Consider the matrix $A =\begin{pmatrix} i & 0 & -1 \\ 1 & -i & 1 \\ 0 & 1 & 2i+1 \end{pmatrix}.$

If the sum of the eigenvalues is $$a+bi$$ and the product of the eigenvalues is $$c+di$$, calculate $$a+b+c+d$$.

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