
complex eigenvalues
i've been given a problem to find the eigenvalues of R = RyRz given theta = pi/2. Ry and Rz are your standard rotation matrixes, so
the real one is simple enough, but when i try to sub in lander i get
(0lander)0 1
1 (0lander)0
0 1 (0lander)
which is evaluating as 
(0  lander)^3 + 1 = 0
so the real solution is 1, as it should be for a rotation. but i cant see where the complex solution could be. should i have kept the equation as trig functions maybe ?
thanks

The eigenvalue equation is $\displaystyle \lambda^31=0$. One solution is $\displaystyle \lambda=1$, so you can divide by the factor $\displaystyle \lambda1$, giving $\displaystyle (\lambda1)(\lambda^2+\lambda+1)=0$. The other two eigenvalues come from solving $\displaystyle \lambda^2+\lambda+1=0$. You can do this by the usual process for solving a quadratic equation, and the solutions are $\displaystyle \lambda=\tfrac12\pm\tfrac{\sqrt3}2i$.
Linguistic note: the Greek letter $\displaystyle \lambda$ is lambda, not lander.