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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