1. ## 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

(0-lander)0 1

1 (0-lander)0

0 1 (0-lander)

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

2. The eigenvalue equation is $\displaystyle \lambda^3-1=0$. One solution is $\displaystyle \lambda=1$, so you can divide by the factor $\displaystyle \lambda-1$, giving $\displaystyle (\lambda-1)(\lambda^2+\lambda+1)=0$. 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.