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**[SOLVED] Complex Eigenvector**

I need to solve for an eigenvector using the complex eigenvalue [tex] -1 + i \sqrt{11} [/tex]. I have a matrix:

[tex]A = \left(\begin{array}{cc}-3 & -5 \\3 & 1\end{array}\right)[/tex]

From the equation [tex] A \vec{V} = \lambda \vec{V} [/tex], where [tex] \vec{V} = (x, y) [/tex] I get :

[tex] -3x - 5y = -1x + i \sqrt{11}x [/tex]

[tex] 3x + y = -1y + i \sqrt{11}y [/tex]

Which gives:

[tex] -2x - i \sqrt{11}x - 5y = 0[/tex]

[tex] 3x + 2y - i \sqrt{11}y = 0 [/tex]

When I solve this system for x and y, I get a solution of (0, 0). The book agrees with the eigenvalue that I found, but has an eigenvector solution of [tex] (-2 + i \sqrt{11}, 3) [/tex]. Can anyone spot what I'm doing wrong?

Any help is appreciated.