True or false? Prove it.
There is a sequence (a_n) of real numbers such that the sequence (1/n e^a_n^i) of complex numbers diverges.
To determine whether the given sequence (1/n e^a_n^i) of complex numbers diverges, we need to examine the behavior of the real sequence (a_n) that is multiplying the imaginary unit i.
To prove whether such a sequence exists or not, we would need to provide a mathematical demonstration or counterexample reflecting the behavior of the sequence (a_n).
However, since the sequence (a_n) is not provided in the question, we cannot definitively determine if the sequence (1/n e^a_n^i) diverges or not. To fully analyze the sequence and make a conclusion, we would need the information about the terms of (a_n).
In summary, without specific information regarding the sequence (a_n), it is not possible to prove whether there exists a sequence where (1/n e^a_n^i) diverges or not.