Solution:

To demonstrate the eigenfunction property of complex exponentials for discrete-time systems, consider an input sequence $x[n]=e^{j \omega n}$ for $-\infty\ltn\lt\infty$, i.e., a complex exponential of radian frequency $\omega$.

The corresponding output of a linear time-invariant system with impulse response h[n] is,

$$ \begin{aligned}\\ y[n] & =\sum_{k=-\infty}^{\infty} h[k] e^{j \omega(n-k)} …