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Let z(k)=cos(2kpi)/10+isin(2kpi)/10,k=1,...

Let `z_(k)=cos(2kpi)/10+isin(2kpi)/10,k=1,2,………..,9`. Then, `1/10{|1-z_(1)||1-z_(2)|……|1-z_(9)|}` equals

A

0

B

1

C

2

D

3

Text Solution

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The correct Answer is:
B
Clearly, `1,z_(1),z_(2),…..,z_(9)` are `10^(th)` roots of unity.
`therefore z_(10)-1=(z-1)(z-z_(1))(z-z_(2))….(z-z_(9))`
`rArr (z-z_(1))(z-z_(2))……(z-z_(9))=1+z+z^(2)+…….+z^(9)`
`rArr (1-z_(1))(1-z_(2))…(1-z_(9))=10`
`rArr 1/10{|1-z_(1))||1-z_(2)|......|1-z_(2)|}=1`
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