$$Ax = 0$$
$$A x= \begin{bmatrix}-6 -2i & 5\\0& 0\end{bmatrix} \begin{bmatrix}x_1\\x_2\end{bmatrix} = \begin{bmatrix}0\\0\end{bmatrix}$$
Simple question, but how do I solve for $x_1$ and $x_2$?
One potential answer is:
$$\begin{bmatrix}x_1\\x_2\end{bmatrix} = \begin{bmatrix}-1+2i\\-2+2i\end{bmatrix}$$
I'm not sure how to get a result like this with complex numbers though. Can I get a detailed explanation on how to do this?
Let $x_1=-6+2i$
$$(-6-2i)(-6+2i)+5x_2=0$$
$$36-(2i)^2+5x_2=0$$
$$40+5x_2=0$$
$$x_2=-8$$