Isn't 100000 such a huge number (Part-10)?

Algebra Level 4

Consider the matrix \[\color{Purple}{\large {Y=\begin{pmatrix} i&0&-2i\\0&100000&0\\2i&0&-i\end{pmatrix}}}\]

If the sum of the eigenvalues can be represented as \(a+bi\) and the product of the eigenvalues can be represented as \(c+di\).

Find the value of \(\color{Blue}{{\dfrac{b+d-c}{a}}}\)

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