Question

Matrix with complex values, need help finding the eigenvalues. Matrix below!

Answer 1

\[\left[\begin{matrix}2 & 2+i \\ -1 & -1-i\end{matrix}\right]\]

I got a polynomial with complex coefficients and apparently I need a refresher in dealing with complex values. \[r^2 - r +ri -i = 0\] I get this polynomial and I'm lost in how to factor this into the roots \[r = 1, -i\]