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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

6a b

B

12 ab

C

`6a^(2) b^(2)`

D

`12 a^(2) b^(2)`

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A
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AAKASH SERIES-COMPLEX NUMBERS-PRACTICE EXERCISE
  1. If 1 , omega , omega^(2) are the cube roots of unity, then prove that ...

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  2. The value of ((- 1 + isqrt3)/(2))^(100) + ((- 1 - isqrt3)/(2))^(100) i...

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  3. If x = a + b , y = a omega^(2) +b omega and z = a omega + b omega^(2) ...

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  4. If alpha , beta are the imaginary cube roots of unity then alpha^(4) +...

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  5. If 1 , omega , omega^(2) are the cube roots of unity , then (a+ b)^(3...

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  6. The value of ((-1 + isqrt3)/(2))^(36) + ( (-1 - isqrt3)/(2))^(36) =

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  7. The solution of the equation |z| - z =1 + 2i is

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  8. If (1 + isqrt2)^(x) = 3^(x) , then its only integral solution is

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  9. If barz = iz^(2) then the number of values of z is

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  10. The number of solutions of z + sqrt2 (| z+ 1|) + i=0

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  11. If the complex number z lies on |z| = 1 then (2)/(z) lies on

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  12. If zbarz=4 then the locus of z is

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  13. Match the items of List - I with those of List-II

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  14. If z = x +iy and P represents z in the Argand plane and mod (2z-3) = 4...

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  15. If z = (lambda + 3) + isqrt( 5 - lambda^(2)) , then the locus of z is...

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  16. If z=(x+iy) and if the point P in the Argarand plane represent z, then...

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  17. If z1=1+2i,z2=2+3i,z3=3+4i, " then " z1,z2and z3 represents the vertic...

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  18. If z is a complex number with |z|ge 5 . Then the least value of |z +...

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  19. (1 + x)^(n) = p(0) + p(1) x + p(2) x^(2) + … + p(n) x^(n) , then p(0)...

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  20. The cube roots of unity when represented on the Argand diagram form th...

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