How do I find complex eigenvectors if I know the complex eigenvalues?

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Assume that we know the complex eigenvalues $\lambda_i$. Is there a way for us to find the complex eigenvectors by finding the nullspace?

$$(A-\lambda_i I)W_i = 0$$

Where $W_i$ is the complex eigenvectors. I don't want to use SVD, because I don't have a SVD solver that can handle imaginary numbers. I'm running everything in C code by the way!

Yes! I have searched for C-code about eigenvectors, but it seems only be for symmetrical matrices.

Notice that this question is about non-symmetrical matrices.