(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

Determine the accumulation points of the following set:

z(sub n)=i^n, (n=1,2,....);

2. Relevant equations

3. The attempt at a solution

My book says z(sub n) does not have any accumulation points. When mapped onto a complex plane, z(sub n) forms a circle. For any set to contained each of its accumulation points, the set has to be closed. And the definition of a closed set is a set containing all of its boundary points. z(sub n) is a close set since the only points of z(sub n) are: i,-1,-i and 1. How can any of those four points not be accumulation points?

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# Accumulation points of a set

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