Can every constant be written in that way?

Question

When we are working in the ring $\mathbb{C}[e^{\lambda x} \mid \lambda \in \mathbb{C}]$ where the elements are of the form $$\sum_{i=0}^n \alpha_i e^{\lambda_i x}$$ where $\alpha_i, \lambda_i \in \mathbb{C}$, can every constant be written in the form $e^b$, for some $b$?