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about to only mathematics

A

`4mpi`

B

`(2mpi)/(n(n+1))`

C

`(4mpi)/(n(n+1))`

D

`(mpi)/(n(n+1))`

Text Solution

Verified by Experts

The correct Answer is:
C
We have,
`(costheta+isintheta)(cos2theta+isin2theta)* * *^(xx)(cosntheta+isintheta)=1`
or `cos(theta+2theta+3theta+* * *+ntheta)+isin(theta+2theta+* * *+ntheta)=1`
or `cos((n(n+1))/(2)theta)+isin((n(n+1))/(2)theta)=1`
or `cos((n(n+1))/(2)theta)=1andsin((n(n+1))/(2)theta)=0`
`rArr (n(n+1))/(2)theta=2mpirArr theta=(4mpi)/(n(n+1)), "where " m in Z`
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