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

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

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

`a^(2)-b^(2)`

`a^(3)+b^(3)`

`a^(3)-b^(3)`

Text Solution

Verified by Experts

Topper's Solved these Questions

DE MOIVRE'S THEOREM
DIPTI PUBLICATION ( AP EAMET)|Exercise EXERCISE 2 SET-1|5 Videos
DE MOIVRE'S THEOREM
DIPTI PUBLICATION ( AP EAMET)|Exercise EXERCISE 2 SET-2|3 Videos
DE MOIVRE'S THEOREM
DIPTI PUBLICATION ( AP EAMET)|Exercise EXERCISE 2 SET-4|3 Videos
COORDINATE SYSTEM (3D)
DIPTI PUBLICATION ( AP EAMET)|Exercise EXERCISE 2 (SPECIAL TYPE QUESTIONS) (SET- 4)|3 Videos
DEFINITE INTEGRATION
DIPTI PUBLICATION ( AP EAMET)|Exercise EXERCISE 2 (SPECIAL TYPE QUSTIONS) CHOOSE THE CORRECT ANSWER FROM THE ALTERNATIVES 1,2,3 OR 4 GIVEN (SET-4)|8 Videos

Similar Questions

Explore conceptually related problems

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)):}

(a-b)(aomega-bomega^(2))(aomega^(2)-bomega)

If a, b are real and x=a+b,y=aomega^(2)+bomega,z=aomega+bomega^(2)" then "x^(2)+y^(2)+z^(2)

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 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 .

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

If 1 , omega , omega^(2) are the cube roots of unity, then prove that ( x + y + z) ( x + y omega + z omega^(2)) ( x + yomega^(2) + z omega) = x^(3) + y^(3) + z^(3) - 3xyz

If x = a + b , y = a omega^(2) +b omega and z = a omega + b omega^(2) , then x^(2) + y^(2) + z^(2) is equal to

(a+2b)^(2)+(aomega+2bomega^(2))^(2)+(aomega^(2)+2bomega)^(2)

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

(a+2b)^(2)+(aomega+2bomega^(2))^(2)+(aomega^(2)+2bomega)^(2)
Text Solution
|
If 1 , omega , omega^(2) are the cube roots of unity , then (a+ b)^(3...
Text Solution
|
If x=a+b,y=aomega+bomega^(2),z=aomega^(2)+bomega then xyz
Text Solution
|
If a, b are real and x=a+b,y=aomega^(2)+bomega,z=aomega+bomega^(2)" th...
Text Solution
|
(1-omega+omega^(2))(1-omega^(2)+omega^(4))(1-omega^(4)+omega^(8))(1-om...
Text Solution
|
If 1 , omega , omega^(2) are the cube roots of unity, then prove that ...
Text Solution
|
(1-omega+omega^(2))(1-omega^(2)+omega^(4))(1-omega^(4)+omega^(8)) …….....
Text Solution
|
If omega is a complex cube root of unity then omega^((1/3+2/9+4/27+......
Text Solution
|
(a+bomega+comega^(2))/(c+aomega+bomega^(2))
Text Solution
|
(1)/(1+2omega)-(1)/(1+omega)+(1)/(2+omega)
Text Solution
|
If omega is a complex cube root of unity, then sin[(omega^(10)+omega^(...
Text Solution
|
If 1,omega,omega^(2) are the cube roots of unity and alpha=omega+2omeg...
Text Solution
|
If alpha, beta are the roots of 1 + x + x^(2)= 0, then the value of al...
Text Solution
|
If x^(2) + x + 1 =0 , then the value of (x + (1)/(x))^(2) + (x^(2) + ...
Text Solution
|
If the cube roots of unity are 1,omega,omega^(2) then the roots of the...
Text Solution
|
If alpha, beta are the non-real cube roots of 2, then alpha^(6)+beta^...
Text Solution
|
If alpha is a non-real root of x^(6)-1=0 then (alpha^(5)+alpha^(3)+alp...
Text Solution
|
If alpha is a non real root of the equation x^(6)-1=0 then (alpha^(2)+...
Text Solution
|
If 1,alpha1,alpha2,…..alpha(n-1) are the n^(th) roots of unity then (1...
Text Solution
|
If 1,alpha1,alpha2,…..alpha(n-1) are the n^(th) roots of unity and n i...
Text Solution
|