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If omega(ne 1) be a cube root of unity a...

If `omega(ne 1)` be a cube root of unity and `(1+omega^(2))^(n)=(1+omega^(4))^(n)`, then the least positive value of n, is

A

2

B

3

C

5

D

6

Text Solution

Verified by Experts

The correct Answer is:
B
We have,
`(1+omega^(2))^(n) = (1+omega^(4))^(n)`
`rArr ((1+omega^(2))/(1+omega^(4)))^(n)=1 rArr ((-omega)/(-omega^(2)))^(n) rArr omega^(2n) =1 rArr n=3,6,9`……..
Hence, the least positive value of n is 3.
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OBJECTIVE RD SHARMA ENGLISH-COMPLEX NUMBERS -Chapter Test
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  5. Prove that the triangle formed by the points 1,(1+i)/(sqrt(2)),a n di ...

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  7. If alpha+ibeta=tan^(-1) (z), z=x+iy and alpha is constant, the locus o...

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  8. If cosA+cosB+cosC=0,sinA+sinB+sinC=0andA+B+C=180^(@) then the value of...

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  9. Find the sum 1xx(2-omega)xx(2-omega^(2))+2xx(-3-omega)xx(3-omega^(2))+...

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  10. The value of the expression (1+(1)/(omega))+(1+(1)/(omega^(2)))+(2+(1)...

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  11. The condition that x^(n+1)-x^(n)+1 shall be divisible by x^(2)-x+1 is ...

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  12. The expression (1+i)^(n1)+(1+i^(3))^(n2) is real iff

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  13. If |{:(6i,3i,1),(4,3i,-1),(20,3,i):}|=x+iy, then (x, y) is equal to

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

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

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  16. Sum of the series sum(r=0)^n (-1)^r ^nCr[i^(5r)+i^(6r)+i^(7r)+i^(8r)] ...

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  17. If az(1)+bz(2)+cz(3)=0 for complex numbers z(1),z(2),z(3) and real num...

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  18. If 2z1-3z2 + z3=0, then z1, z2 and z3 are represented by

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  19. If Re((z+4)/(2z-1)) = 1/2 then z is represented by a point lying on

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  20. The vertices of a square are z(1),z(2),z(3) and z(4) taken in the anti...

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  21. Let lambda in R . If the origin and the non-real roots of 2z^2+2z+lam...

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