We know that for a curve $X$, any object $\mathcal{E}^{\bullet}$ in the derived category $D^b_{\text{coh}}(X)$ is formal, i.e. $\mathcal{E}^{\bullet}$ is quasi-isomporphic to the direct sum of its cohomology sheaves. The reason is that the cohomological dimension of $X$ is $1$. We can see Corollary 3.15 of Daniel Huybrechts' book "Fourier–Mukai transforms in algebraic geometry" for details.

Now could we find an "easy" example of object in $D^b_{\text{coh}}(\mathbb{P}^2)$ which is not formal? In particular, could we find a complex of sheaves on $\mathbb{P}^2$ of length $2$ with coherent cohomology which is not quasi-isomorphic to the direct sum of its cohomology sheaves?