(1)/(1+2omega)-(1)/(1+omega)+(1)/(2+omeg...

`(1)/(1+2omega)-(1)/(1+omega)+(1)/(2+omega)`

`omega`

`omega^(2)`

`a^(2)+b^(2)`

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If 1 , omega , omega^(2) are the cube roots of unity, then prove that 1/(2 + omega) + 1/(1+2 omega) = 1/(1 + omega) .

If 1, omega , omega^(2) are the cube roots of unity, then prove that 1/(2 + omega) + 1/(1 + 2 omega) = 1/( 1 + omega) .

(1 - omega) (1 - omega^(2)) (1 - omega^(4)) (1 - omega^(5)) (1 - omega^(7)) (1 - omega^(8)) =

(1 + omega) (1 + omega^(2)) (1 + omega^(3)) (1 + omega^(4)) (1 + omega^(5)) (1 + omega^(6)) …. (1 + omega^(3n)) =

Arrange the following values in descending order A)(1+omega)(1+omega^2)(1+omega^4)(1+omega^8) B) (1-omega+omega^2)^7+(1+omega-omega^2)^7 C)(1-omega)(1-omega^2)(1-omega^4)(1-omega^8) D) (1-omega+omega^2)(1-omega^2+omega^4)

If omega_0 , omega_1 , ………, omega_( n - 1) are the nth roots of unity then (1 + 2 omega_0) ( 1 + 2 omega_1) (1 + 2 omega_2)…..(1 + 2omega_(n - 1) ) =

(1 - omega + omega^(2)) ( 1 - omega^(2) + omega^(4)) ( 1- omega^(4) + omega^(8)) to 2n factors =

If 1 , omega , omega^(2) are the cube roots of unity, then prove that (2 - omega)(2 -omega^(2)) (2 - omega^(10)) ( 2 - omega^(11)) = 49 .

DIPTI PUBLICATION ( AP EAMET)-DE MOIVRE'S THEOREM-EXERCISE 1

If omega is a complex cube root of unity then omega^((1/3+2/9+4/27+......
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(a+bomega+comega^(2))/(c+aomega+bomega^(2))
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(1)/(1+2omega)-(1)/(1+omega)+(1)/(2+omega)
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If omega is a complex cube root of unity, then sin[(omega^(10)+omega^(...
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If 1,omega,omega^(2) are the cube roots of unity and alpha=omega+2omeg...
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If alpha, beta are the roots of 1 + x + x^(2)= 0, then the value of al...
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If x^(2) + x + 1 =0 , then the value of (x + (1)/(x))^(2) + (x^(2) + ...
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If the cube roots of unity are 1,omega,omega^(2) then the roots of the...
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If alpha, beta are the non-real cube roots of 2, then alpha^(6)+beta^...
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If alpha is a non-real root of x^(6)-1=0 then (alpha^(5)+alpha^(3)+alp...
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If alpha is a non real root of the equation x^(6)-1=0 then (alpha^(2)+...
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If 1,alpha1,alpha2,…..alpha(n-1) are the n^(th) roots of unity then (1...
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If 1,alpha1,alpha2,…..alpha(n-1) are the n^(th) roots of unity and n i...
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1,alpha1,alpha2,alpha3…..alpha(n-1) are the n^(th) roots of unity and ...
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If 1,z1z2,……z(n-1) are the n^th roots of unity, then (1-z1)(1-z2)…..(1...
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If alpha is an n^(th) root of unity then prove that 1+2alpha+3alpha^2+...
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If 1,alpha,alpha^2,…...,alpha^(n-1) are the n^(th) roots of unity, the...
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Statement-I : If xn=cos(pi//2^n)+isin (pi//2^n) then x1.x2.x3…..=-...
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If X(n)="cos"(pi)/(2^(n))+"isin"(pi)/(2^(n)), then x(1), x(2), x(3)......
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If x(n)=cos((pi)/(4^(n)))+i sin ((pi)/(4^(n))), then x(1), x(2), x(3)....
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