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## Homework Statement

Given A = [ (3,-7),(1,-2) ] and λ

_{a}= [itex]\frac{1}{2}[/itex] + i [itex]\frac{\sqrt{3}}{2}[/itex] find a single eigenvector which spans the eigenspace.

## Homework Equations

## The Attempt at a Solution

So I row reduced the matrix to get [(2, -5 + i[itex]\sqrt{3}[/itex]),(0,0 ] and from here we can write a solution as (x1,x2)=x2((1/2,1)) however that is not a complex eigenvector, it is just a real v etor. So Somewhere along the lines I am making a mistake in understanding how you solve for a complex eigenvector. I can do this in Rn very well, but this is throwing me off.