Zariski density of the complex exponential graph
= Zariski density of the complex exponential graph
The graph $\{(x,e^x):x\in\mathbb C\}$ is Zariski dense in $\mathbb A^2_\mathbb C$. If $\sum_jp_j(x)e^{jx}=0$, repeated application of $D-m$ removes the largest exponential term while acting injectively on the others, proving inductively that every $p_j$ vanishes.