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If alpha,betaandgamma are the cube roots...

If `alpha,betaandgamma` are the cube roots of `P(p)lt0),` then for any `x, y,andz,(xalpha+ybeta+zgamma)/(xbeta+ygamma+zalpha` is equal to

A

`omega,omega^(2)`

B

`-omega,-omega^(2)`

C

`1,-1`

D

none of these

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The correct Answer is:
a
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OBJECTIVE RD SHARMA ENGLISH-COMPLEX NUMBERS -Exercise
  1. If (a(1)+ib(1))(a(2)+ib(2))………………(a(n)+ib(n))=A+iB, then sum(i=1)^(n) ...

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  2. If cosalpha+2cosbeta+3cosgamma=sinalpha+2sinbeta+3singamma=0,t h e nt ...

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  3. If alpha,betaandgamma are the cube roots of P(p)lt0), then for any x, ...

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  4. prove that tan(i" In"((a-ib)/(a+ib)))=(2ab)/(a^(2)-b^(2)) (where a, ...

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  5. Find the relation if z1, z2, z3, z4 are the affixes of the vertices of...

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  6. The locus of the points representing the complex numbers z for which |...

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  7. For n=6k, k in z, ((1-isqrt(3))/(2))^(n)+((-1-isqrt(3))/(2))^(n) has t...

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  8. The product of all values of (cosalpha+isinalpha)^(3//5) is

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  9. If C^(2)+S^(2)=1, then (1+C+iS)/(1+C-iS) is equal to

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  10. The centre of a square ABCD is at z=0, A is z(1). Then, the centroid o...

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  11. The number of solutions of the system of equations "Re(z^(2))=0, |z|=2...

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  12. The vector z=-4+5i is turned counter clockwise through an angle of 180...

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  13. The value of [sqrt(2)(cos(56^(@)15^('))+isin(56^(@)15^('))]^(8), is

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  14. Find the complex number z satisfying the equation |(z-12)/(z-8i)|= (5)...

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  15. The vertices B and D of a parallelogram are 1-2i and 4-2i If the diago...

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  16. If the complex number z(1) " and " z(2) are such that arg (z(1)) - ar...

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  17. The join of z(1)=a+ib and z(2)=1/(-a+ib) passes through

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  18. If z(1),z(2),z(3),z(4) are the affixes of the four points in the Ar...

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  19. The value of sum(r=1)^(8)(sin((2rpi)/9)+icos((2rpi)/9)), is

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  20. If z(1),z(2),z(3),…,z(n) are n,nth roots of unity, then for k=1,2,3,…n

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