Find the eigenvectors of the matrix

I've already found the eigenvalues which come out to be 1, 2+i and 2-i.

To find the eigenvectors I have to find v such that .

I already found the eigenvector for . I'm having trouble with it for the complex cases.

Here's my working for :

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The only vector that satisfies these conditions is the zero matrix which cannot be an eigenvector by definition!