Let $a_{1}, \ldots, a_{n}$ be distinct complex numbers. Show that the functions $e^{a_{1} z}, \ldots, e^{a_{n} z}$ are linearly independent over $\mathbb{C}$.
Let $a_{1}, \ldots, a_{n}$ be distinct complex numbers. Show that the functions $e^{a_{1} z}, \ldots, e^{a_{n} z}$ are linearly independent over $\mathbb{C}$.