Question

The $n^{th}$ roots of unity are in
[Orissa JEE 2004]

• A.
  A.P.
• B. G.P.
• C. H.P.
• D. None of these

Answer 1

The correct option is B

G.P.

$x^n=1=(cos0+isin{0}^o$ ) = cos2r\pi + i sin 2r\pi = e^{i2r\pi} \)
$\Rightarrow x=e^{i\left(2r\pi /n\right)},r=0,1,2.....$
Obviously the roots are $1,e^{2\pi i/n},e^{4\pi i/n}......$ which are obviously in G.P. with common ratio $e^{2\pi i}/n.$