(a+bomega+comega^(2))/(c+aomega+bomega^(...

`(a+bomega+comega^(2))/(c+aomega+bomega^(2))`

`omega`

`omega^(2)`

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

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If 1 , omega + omega^(2) are the cube roots of unity prove that (i) (1 - omega + omega^(2))^(6) + (1 - omega^(2) + omega)^(6) = 128 = ( 1 - omega + omega^(2))^(7) + ( 1 + omega - omega^(2))^(7) (ii) ( a+ b) ( aomega+b omega^(2))( a omega^(2) + b omega) = a^(3) + b^(3) (iii) x^(2) + 4x + 7 = 0 " where " x = omega - omega^(2) - 2 .

If x=a+b,y=aomega+bomega^(2),z=aomega^(2)+bomega then xyz

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If 1 , omega , omega^(2) are the cube roots of unity prove that (a + b) ( a omega + b omega^(2))(aomega^(2) + b omega) = a^(3) + b^(3)

If x=a+b,y=aomega+bomega^2,z=aomega^2+bomega then match the following {:(I.,x+y+z,"a)"a^3+b^3),(II.,xyz,"b)"3(a^3+b^3)),(III.,x^2+y^2+z^2,"c)"6ab),(IV.,x^3+y^3+z^3,"d)"0),(,,"e)"2(a^3+b^3)):}

If C = 60 ^(@) then show that (b)/( c^(2) -a^(2)) + (a)/( c^(2) - b^(2)) =0.

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

(1-omega+omega^(2))(1-omega^(2)+omega^(4))(1-omega^(4)+omega^(8)) …….....
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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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