The n th roots of unity are in

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Question: Answered & Verified by Expert

The

n^{th}

roots of unity are in

MathematicsComplex NumberJEE Main

Options:

A $AP$
B $GP$
C $HP$
D None of these

Solution:

2701 Upvotes Verified Answer

The correct answer is:

GP

Let $x = 1$

$= \cos 0 ° + i \sin 0 °$

$\Rightarrow x^{1 / n} = e^{i (2 π r) / n}; r = 0, 1, 2, \dots$

Then, the roots are $1, e^{\frac{2 π i}{n}}, e^{\frac{4 π i}{n}}, \dots$ which are clearly on $GP$ with common ratio $e^{2 π i / n}$

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