One part is easy as exponential function is continuous but the other part is not able to solve ( as we know that Log is not continuous).

=================

how you define the complex logarithm ?

– Tsemo Aristide

Oct 20 at 18:00

By convergence, did you mean convergence to a nonzero value?

– zhw.

Oct 20 at 18:01

The domain for a branch of the logarithm is obtained by removing from the plane a ray (emanating from the origin). Since some of your znz_{n}’s may be on that ray, you need to use two branches of the logarithm, and treat the convergence issues on both of them.

– user8960

Oct 20 at 18:09

=================

=================