Sorry, if this is the wrong subforum, firstly.

So I have a dynamical system with fixed points $\displaystyle (0,0)$, $\displaystyle (1,0)$ and $\displaystyle (-1,0)$.

The bit I'm stuck on is this; I have the Jacobian matrix for $\displaystyle (1,0)$ and $\displaystyle (-1,0)$ as $\displaystyle A=\left( \begin{array}{cc} 0 & 1 \\ -2 & 1 \end{array}\right)$ (so the trace $\displaystyle \tau=1$ and the determinant $\displaystyle \delta=2$) and the eigenvalues as $\displaystyle \lambda_1=\frac{1}{2}(1_+7i)$ and $\displaystyle \lambda_2=\frac{1}{2}(1-7i)$.

To find the eigenvectors $\displaystyle \mathbf{U}$ and $\displaystyle \mathbf{V}$ I know I need to solve

$\displaystyle A=\left( \begin{array}{cc} 0 & 1 \\ -2 & 1 \end{array}\right) \left( \begin{array}{c} U_1 \\ U_2 \end{array} \right)=\frac{1}{2}(1+7i)\left( \begin{array}{c} U_1 \\ U_2 \end{array} \right)$

and

$\displaystyle A=\left( \begin{array}{cc} 0 & 1 \\ -2 & 1 \end{array}\right) \left( \begin{array}{c} V_1 \\ V_2 \end{array} \right)=\frac{1}{2}(1-7i)\left( \begin{array}{c} V_1 \\ V_2 \end{array} \right)$

and this is what I'm stuck on. I've found both lines of the simultaneous equations to be

$\displaystyle U_2=\frac{1}{2}(1+7i)U_1$

$\displaystyle -2U_1+U_2=\frac{1}{2}(1+7i)U_2$

but I can't get anywhere with it. I did give it a go and got $\displaystyle U_1=0$ but I get the feeling that's not right this was never my strong point when we initially learned it, but I think it's the complex number that's confusing me. Any ideas? Cheers in advance.