Question

Which of the following expressions is a sixth root of unity?

Answer 1

-1 for apex i just answered this question and got it right

Answer 2

Let sixth root of unity be x

So $x^{6}=1$

$x^6-1=0$

$(x^3)^2-1^2=0$

$(x^3-1)(x^3+1)=0$$x^3-1=0 or x^3+1=0$

$(x-1)(x^2+x+1)=0 or (x+1)(x^2-x+1)=0$$x-1=0 or x^2+x+1=0 or x+1=0 or x^2-x+1=0$

Using Quadratic formula for the quadratic equations we get

$x=1 or x=\frac{-1\pm\sqrt{1-4} }{2} or x = -1 or x=\frac{1\pm\sqrt{1-4} }{2}$

$x = 1 or x=\frac{-1\pm\sqrt{3}i }{2} or x = -1 or x=\frac{1\pm\sqrt{3}i }{2}$

Only 1, out of the given option is the sixth root of unity.