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If 1 , omega , omega^(2) are the cube r...

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

A

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

B

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

C

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

D

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

Text Solution

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The correct Answer is:
B
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AAKASH SERIES-COMPLEX NUMBERS-PRACTICE EXERCISE
  1. If x = a + b , y = a omega^(2) +b omega and z = a omega + b omega^(2) ...

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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  17. (1 + x)^(n) = p(0) + p(1) x + p(2) x^(2) + … + p(n) x^(n) , then p(0)...

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

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  19. If a , b , c in R such that a + b + c= 0 and az(1) + bz(2) + cz(3) = ...

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  20. In the Argand plane the area in square units of the triangle formed by...

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