Which of the following is equal to `root(3)(-1)?`

Options

A. `(sqrt(3)+sqrt(-1))/( 2)`
B. `(-sqrt(3)+sqrt(-1))/(sqrt(-4))`
C. `(sqrt(3)-sqrt(-1))/(sqrt(-4))`
D. `-sqrt(-1)`

Answer

B

Explanation

`x =root(3)(-1)`
`rArr x^(3)=-1`
`rArr -x^(3)=1`
`rArr-x=1,omega,omega^(2)` ltbgt `rArr x=-1,-omega,-omega^(2)`
`=-1,(1+sqrt3i)/(2),(1-sqrt3i)/(2)`
`=-1,(-sqrt3+i)/(2i),(sqrt3+i)/(2i)`
`=-1,(-sqrt3+sqrt(-1))/(sqrt(-4)),(sqrt(3)+(sqrt(-1)))/(sqrt(-4))`