a.) Prove that if $x ^+_- iy$ is a complex conjugate pair of eigenvectors of a real matrix A corresponding to complex conjugate eigenvalues $\mu ^+_- iv$ with $v\ne 0$, then x and y are linearly independent real vectors.
b.) More generally, if $v_j=x_j {^+_-} iy_j$, $j=1,...,k$ are complex conjugate pairs of eigenvectors corresponding to distinct pairs of complex conjugate eigenvalues $\mu_j {^+_-} iv_j,v_j \ne 0$, then the real vectors $x_1,...,x_k,y_1,...,y_k$ are linearly independent.
How will I be able to prove these?