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A discrete system is represented by the difference equation

$\begin{bmatrix} X_1(k+1)\\ X_2(k+2) \end{bmatrix}=\begin{bmatrix} a & a-1\\ a+1 & a \end{bmatrix}\begin{bmatrix} X_1(k)\\X_2(k) \end{bmatrix}$

It has initial conditions $X_1(0)$ = $1$; $X_2(0)$ = $0$. The pole locations of the system for $a$ = $1$, are

- $1\pm j0$
- $-1\pm j0$
- $\pm 1+j0$
- $0\pm j1$

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