Complex Eigenvalues

Algebra Level 5

Consider the matrix A=(i011i1012i+1).A =\begin{pmatrix} i & 0 & -1 \\ 1 & -i & 1 \\ 0 & 1 & 2i+1 \end{pmatrix}.

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

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