Assertion (A): `((-1+sqrt(-3))/(2))^(29)+((-1-sqrt(-3))/(2))^(29)=-1`
Reason (R ) `omega^(2)=-1`

Options

A. Both A and R are true and R is the correct explanation of A
B. Both A and R are true but R is not the correct explanation of A
C. A is true but R is false.
D. A is false but R is true.

Answer

C

Explanation

Consider `[(-1+sqrt(-3))/(2)]^(29)+[(-1-sqrt(-3))/(2)]^(29)`
`[(-1+sqrt(3i))/(2)]+[(-1sqrt(3i))/(2)]^(29)`
`(omega)^(29)+(omega^(2))^(29)=omega^(27).omega^(2)+(omega^(3))^(19).omega`
`=(omega^(3))^(9)omega^(2)+(omega^(3))^(19).omega`
`=1.omega^(2)+1.omega" "(becauseomega^(3)=1)`
`=omega^(2)+omega=-1`
`(R) omega^(2)ne-1`
A is true but R is false.