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If z is a complex number satisfying z + ...

If z is a complex number satisfying `z + z^-1 = 1` then `z^n + z^-n , n in N`, has the value

A

`2(-1)^(n)`, where n is a multiple of 3

B

`(-1)^(n)`, where n is not a multiple of 3

C

`(-1)^(n+1)`, where n is not a multiple of 3

D

none of these

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a
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OBJECTIVE RD SHARMA-COMPLEX NUMBERS -Exercise
  1. If arg (z(1)z(2))=0 and |z(1)|=|z(2)|=1, then

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  2. If omega is a complex cube root of unity, then ((1+i)^(2n)-(1-i)^(2n))...

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  3. If z is a complex number satisfying z + z^-1 = 1 then z^n + z^-n , n i...

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

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  5. If z is nonreal root of [-1]^[1/7] then,find the value of z^86+z^175+z...

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

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

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

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  9. The roots of the cubic equation (z + alpha beta)^3 = alpha^3 , alpha ...

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  10. The roots of the cubic equation (z + alpha beta)^3 = alpha^3 , alpha ...

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  11. If alpha,beta,gamma and delta are the equation x^(4)-1 = 0, then the v...

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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 equation |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. Let z=1-t+isqrt(t^2+t+2), where t is a real parameter.the locus of the...

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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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