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The pole-zero diagram of a casual and stable discrete-time system is shown in the figure. The zero at the origin has multiplicity $4$. The impulse response of the system is $h[n]$. If $h[0]=1$, we can conclude

- $h[n]$ is real for all $n$
- $h[n]$ is purely imaginary for all $n$
- $h[n]$ is real for only even $n$
- $h[n]$ is purely imaginary for only odd $n$