Let $A_1,A_2,A_3$ and $\alpha_1,\alpha_2,\alpha_3$ be real constants.
Suppose the equation $A_1e^{i\alpha_1x}+A_2e^{i\alpha_2x}=A_3e^{i\alpha_3x}$ holds $\forall x\in\mathbb{R}$. (where $i^2=-1$)
Can we find the relation between the constants $\alpha_1,\alpha_2$ and $\alpha_3$?