I am solving for the eigenvector of the following array:

$\displaystyle \left(\begin{array}{cc}1-8i&-13\\5&-1-8i\end{array}\right)\left(\begin{array}{cc}n_1\\n_ 2\end{array}\right)=\left(\begin{array}{cc}0\\0\en d{array}\right)$

The rows are multiples of each other, and if I understand this either row can be solved for the eigenvector. If I use the bottom row I get

$\displaystyle \left(\begin{array}{cc}1+8i\\5\end{array}\right)$

If I use the top row I get

$\displaystyle \left(\begin{array}{cc}13\\1-8i\end{array}\right)$

Is this correct? Are those two vectorsequal? I do not have this problem when the eigenvalues are all real numbers.