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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

4

Text Solution

Verified by Experts

The correct Answer is:
B
`Z_(k)=e^(i(2k pi)/(10))`
`Z^(10)-1=(Z-1)(Z-Z_(1))(Z-Z_(2))….(Z-Z_(9))`
`lim_(Z to 1)(Z^(10-1))/(Z-1)= lim_(z to 1)(Z-Z_(1))(Z-Z_(2))…(Z-Z_(9))`
`10=(1-Z_(1))(1-Z_(2))….(1-Z_(9))`
`1=(|1-Z_(1)||1-Z_(2)|…|1-Z_(9)|)/(10)`
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