Complex eigenvalue Question: Suppose  is a 3×3 matrix with real entries that has a complex eigenvalue −1+8 with corresponding eigenvector 
\begin{bmatrix}
1-2i\\ 
-1\\ 
8i
\end{bmatrix}
Find another eigenvalue and eigenvector for .
What should i do?

$A$ has real entries so $\bar{A}=A$. Now just conjugate $Av=\lambda v$ you get that $\bar{\lambda}$ is an eigenvalue corresponding to $\bar{v}$. (Remember this is only true because $A$ has real entries).
So $-1-8i$ is an eigenvalue with eigenvector $(1+2i,-1,-8i)^T$
