`((-1+isqrt(3))/(2))^(3pi) + ((-1-isqrt(3))/(2))^(3pi)` का मान क्या है जहाँ `I = sqrt(-1)` है ?

Options

A. 3
B. 2
C. 1
D. 0

Explanation

दिया हैं,
`((-1+isqrt(3))/(2))^(3n) + ((-1-isqrt(3))/(2))^(3n)`
`= (omega)^(3n) + (omega^(2))^(3n)`
`[ :' omega = (-1+isqrt(3))/(2), omega^(2) = ((-1-isqrt(3))/(2))]`
`= (omega^(2))^(n) + (omega^(3))^(2n)`
`(1)^(n) + (1)^(2n) , [ :' omega^(5) = 1]`
`= 1 + 1 = 2`