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if z = (sqrt 3 ) /(2) + (i)/(2) ( ...

if ` z = (sqrt 3 ) /(2) + (i)/(2) ( i=sqrt ( -1) )`, then ` ( 1 + iz + z^5 + iz^8)^9 ` is equal to:

A

` ( - 1 + 2 i) ^ 9 `

B

` 0 `

C

` -1 `

D

` 1 `

Text Solution

Verified by Experts

` z = (sqrt 3 )/(2) + (i)/(2) = cos "" (pi ) /(6) = isin "" (pi )/(6) rArr z ^ 5 = ( - sqrt 3 )/(2 ) + (i)/(2) `
` z ^8 = - (1)/(2) - (isqrt3)/(2) rArr (1 + iz + z^5 +iz^8)^9 `
` = ((1)/(2) + (isqrt3 )/(2))^9 = cos 3pi + i sin 3pi `
` = -1 `
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