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If i = sqrt(-1), omega is non-real cube ...

If `i = sqrt(-1), omega` is non-real cube root of unity then `((1 + i)^(2n) - ( 1 - i ) ^(2n) )/((1 + omega^(4) - omega^(2) ) ( 1- omega^(4) + omega^(2)))` is equal to :

A

0, if n is an even integer

B

0 for all `n in Z`

C

`2^(n-1)i` for all `n in N`

D

none of these

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The correct Answer is:
A
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OBJECTIVE RD SHARMA ENGLISH-COMPLEX NUMBERS -Exercise
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  2. If arg (z(1)z(2))=0 and |z(1)|=|z(2)|=1, then

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  3. If i = sqrt(-1), omega is non-real cube root of unity then ((1 + i)^(2...

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  4. If z is a complex number satisfying z+z^(-1) =1 " then " z^(n) + z...

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  5. x^(3m) + x^(3n-1) + x^(3r-2), where, m,n,r in N is divisible by

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  6. If z is nanreal root of ""^(7)sqrt(-1), then find the value of z ^(86...

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  7. The locus of point z satisfying Re(z^(2))=0, is

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  8. The curve represented by "Im"(z^(2))=k, where k is a non-zero real num...

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  9. If log(tan30^@)[(2|z|^(2)+2|z|-3)/(|z|+1)] lt -2 then |z|=

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  10. The roots of the cubic equation (z+ ab)^(3) = a^(3), such that a ne 0...

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  11. The roots of the cubic equation (z+ ab)^(3) = a^(3), such that a ne 0...

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  12. If omega is a complex cube root of unity, then the equation |z- omega|...

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  13. If omega is a complex cube root of unity, then the equationi |z-omega|...

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  14. The equation zbarz+(4-3i)z+(4+3i)barz+5=0 represents a circle of radiu...

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  15. z is such that a r g ((z-3sqrt(3))/(z+3sqrt(3)))=pi/3 then locus z is

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  16. about to only mathematics

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  17. If |z-4+3i| leq 1 and m and n be the least and greatest values of |z...

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  18. If 1,alpha,alpha^(2),………..,alpha^(n-1) are the n, n^(th) roots of unit...

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  19. If z(r)(r=0,1,2,…………,6) be the roots of the equation (z+1)^(7)+z^7=0...

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  20. The least positive integer n for which ((1-i)/(1-i))^n=2/pi "sin"^(-1)...

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