Let `A_0,A_1,.......,A_(n-1)` be a n-sided polygon with vertices as `1,omega,omega^2,.......,omega^(n-1)` Let `B_1, B_1,..... B_(n -1)` be another polygon with vertices `1 , 1 + omega, 1 +omega^2,........,1+omega^(n-1)[omega=cos((2pi )/n)+i sin n((2pi)/n)] ` for `n=4,(A rdot(A_0, A_1, A_2, A_3))/(A r*(B_0, B_1, , B_3))` is `lambda` then

Options

A. `[lamda]gt3`
B. `(3lamda)/2 epsilon I^(+)`
C. `([lamda])/3 epsilon I^(+)`
D. `lamda` is irrational

Answer

B

Explanation

`Ar.(B_(0),B_(1),………B_(n-1))=n/4 cot ((pi)/n)`
`Ar(A_(0)A_(1).A_(n-1))=n/s "sin" (2pi)/n`
`:.(Ar.(A_(0)A_(1).A_(n)))/(Ar.(B_(0)B_(1)………B_(n)))=(n"sin" (pi)/n "cos" (pi)/n)/(n/4"cot" (pi)/n)=4"sin"^(2) (pi)/n`