$\mathbf {The \ Problem \ is}:$ Find all values of the positive integer $n$ such that $Q(e^{\frac {2πi}{n}})$ contains $i.$
$\mathbf {My \ approach}:$ I could only think that $4$ divides $n$ as $Q(e^{\frac {2πi}{4n}})$ contains $(e^{\frac {2πi}{4n}})^n = i.$ But, are these the only values of $n?$
I couldn't approach how to find other values .
A small hint is warmly appreciated . Thanks in advance .