Given the rotation matrix (cos x -sin x)
sinx cosx
(supposed to by a 2x2 matrix)
I have to find the complex eigenvalues and eigenvectors when sin x not=0
Dont know if i'm going the right way but I have p(L) = det(cosx-L -sin x)
sin x cosx-L
= (cosx-L)^2 - (-sinx)^2 = (cosx)^2-2Lcosx+L^2+(sinx)^2
=L^2-2Lcosx+1
I dont know where to go from here, thanks