I am trying to prove the following:
Let $R=\mathbb{C}[t]/(t^2)$ and $ N=R/(t)=\mathbb{C}[t]/(t)$, define $f:R\to R$ by $f(r)=rt$. Then the following two chain complexes have the same cohomology for each $i$
$C=(\dots \to 0 \to R \to^{f} R \to 0 \to \dots), N=(\dots \to 0 \to N \to^{0} N \to 0 \to \dots)$
Show that there is no quasi isomorphism from $C$ to $D$ nor from $D$ to $C$.