If $\left\{ a _ { n } \right\} _ { n = 1 } ^ { \infty } , \left\{ b _ { n } \right\} _ { n = 1 } ^ { \infty }$ are two sequences of positive real numbers with the first converging to zero, and the second diverging to $\infty$, then the sequence of complex numbers $c _ { n } = a _ { n } e ^ { i b _ { n } }$ also converges to zero.