Let z(k+1) = z(k) be a complex scalar iterative equation with = u + iv. Show

Let z(k+1) = λz(k) be a complex scalar iterative equation with λ = u + iv. Show that its real and imaginary parts x(k) = Rez(k), y(k) = Imz(k) satisfy a two-dimensional real linear iterative system. Use the eigenvalue method to solve the real 2 × 2 system, and verify that your solution coincides with the solution to the original complex equation.