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Let arg(z(k))=((2k+1)pi)/(n) where k=1,2...

Let `arg(z_(k))=((2k+1)pi)/(n)` where `k=1,2,………n`. If `arg(z_(1),z_(2),z_(3),………….z_(n))=pi`, then `n` must be of form `(m in z)`

A

`4m`

B

`2m-1`

C

`2m`

D

None of these

Text Solution

Verified by Experts

The correct Answer is:
B
`(b)` `arg(z_(1),z_(2),z_(3)……….z_(n))=pi`
`impliesarg(z_(1))+arg(z_(2))+….+arg(z_(n))=pi+-2mpi`, `m in I`
`implies (pi)/(n)[3+5+7+….+(2n+1)]=pi+-2mpi`
`implies(pi)/(n)[(n)/(2)[6+2(n-1)]]=pi+-2mpi`
`implies3+n-1=1+-2m`
`impliesn=-1=1+-2m`
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