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> Why does $$\left (\frac{3+4i}{5} \right)^n$$ not converge?
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I have calculated $\left |\left (\frac{3+4i}{5} \right)^n \right|$ and I got $1$. But in the Solutions they wrote without further comment that this sequence does not converge.

I understood that $|\cdot|\neq0$ is not a necessary condition for convergence because $|(-1)^n|=1$ but does not converge.

But I still don't know how I can prove that the named sequence is not convergent.