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Values (s)(-i)^(1//3) is/are (sqrt(3)-i)...

Values `(s)(-i)^(1//3)` is/are `(sqrt(3)-i)/2` b. `(sqrt(3)+i)/2` c. `(-sqrt(3)-i)/2` d. `(-sqrt(3)+i)/2`

A

`s(sqrt(3)-i)/(2)`

B

`(sqrt(3) +i)/(2)`

C

`(-sqrt(3)-i)/(2)`

D

`(-sqrt(3)+i)/(2)`

Text Solution

Verified by Experts

The correct Answer is:
A, C
`(-i)^(1//3) = (i^(3))^(1//3) = i,iomega,iomega^(2)`
where `omega = (-1+sqrt(3)i)/(2)`
Hence, values are i, `(-sqrt(3-i)//2)(sqrt(3-i))//2`
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