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Let 1, z(1),z(2),z(3),…., z(n-1) be the ...

Let 1, `z_(1),z_(2),z_(3),…., z_(n-1)` be the nth roots of unity. Then prove that `(1-z_(1))(1 - z_(2)) …. (1-z_(n-1))= n`. Also,deduce that `sin .(pi)/(n) sin.(2pi)/(pi)sin.(3pi)/(n)...sin.((n-1)pi)/(n) = (pi)/(2^(n-1))`

A

n

B

`(-1)^(n).n`

C

zero

D

None of these

Text Solution

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The correct Answer is:
A
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