Show that $f(n) = \left(\frac{\sqrt 2}{2}(1+i)\right)^n$ diverges I am having this sequence:
$$f (n)= \left( \frac{\sqrt 2}{2}(1+i)\right)^n$$
I think it is divergent, because I found a subsequence that is divergent:
The subsequence $4n$ shows that the sequence alternates between $1$ and  $-1$.

Questions:


*

*Is this correct?

*How can I write my reflections down in a formally correct way?


It is correct. Since
$$|f(4n+4)-f(4n)|=2\quad\forall n\in\Bbb N$$
the sequence is not a Cauchy sequence, and hence it diverges.
