Impulse response function from pole-zero graph
You don't need the zeros, you just need to understand the relation between poles and the corresponding time domain function. A real-valued pole $s_{\infty}=\sigma$ corresponds to an exponential function

$$\frac{k}{s-\sigma}\Longleftrightarrow ke^{\sigma t},\qquad t&gt;0$$

A double real-valued pole corresponds to an exponential multiplied by $t$:

$$\frac{k}{(s-\sigma)^2}\Longleftrightarrow kte^{\sigma t},\qquad t&gt;0$$

[You can look up how this generalizes to poles of higher order.]

A pair of complex conjugate poles $s_{\infty}=\sigma\pm j\omega$ corresponds to a sinusoid with frequency $\omega$ multiplied by an exponential:

$$ke^{\sigma t}\cos(\omega t+\phi),\qquad t&gt;0$$

The scaling $k$ and the phase $\phi$ depend on the numerator of the Laplace transform, but here they are irrelevant.

So for the given pair of complex conjugate poles, we know that the corresponding time domain function must be an exponentially damped ($\sigma=-1&lt;0$) sinusoid with frequency $\omega=2$.