Let be nonzero complex numbers. Suppose exists, and .

1. Show that if one of the series and converges absolutely, then so does the other.

2. What if or ?

For #1, I assume converges absolutely and trying to prove converges absolutely. That is, there exists such that for .

I tried to use what I have to prove this, but not getting what I want. Can I get some help?

I don't know #2...