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If z^2+z+1=0 where z is a complex number...

If `z^2+z+1=0` where `z` is a complex number, then the value of `(z+1/z)^2+(z^2+1/z^2)^2+....+(z^6+1/z^6)^2` is

A

18

B

54

C

6

D

12

Text Solution

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The correct Answer is:
D
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ARIHANT MATHS-COMPLEX NUMBERS-Exercise (Questions Asked In Previous 13 Years Exam)
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  2. Find the value of sum(k=1)^10[sin((2pik)/(11))-icos((2pik)/(11))],wher...

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  3. If z^2+z+1=0 where z is a complex number, then the value of (z+1/z)^2+...

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  4. A man walks a distance of 3 units from the origin towards north-east t...

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  5. If |z|=1 and z!=+-1, then all the values of z/(1-z^2) lie on

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  6. If abs(z+4) le 3, the maximum value of abs(z+1) is

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  7. Let A, B, C be three sets of complex number as defined below: A={z:Img...

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  8. Let A,B and C be three sets of complex numbers as defined below: {:(,A...

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  9. Let A,B and C be three sets of complex numbers as defined below: {:(,A...

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  10. A particle P starts from the point z0=1+2i , where i=sqrt(-1) . It mov...

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  11. If the conjugate of a complex numbers is 1/(i-1), where i=sqrt(-1). Th...

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  12. Let z=x+i y be a complex number where xa n dy are integers. Then, the ...

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  13. Let z=costheta+isintheta. Then the value of sum(m->1-15)Img(z^(2m-1...

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  14. If |Z-4/Z|=2 then maximum value of |Z| is equal to

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  15. Let z(1) and z(2) be two distinct complex numbers and z=(1-t)z(1)+iz(2...

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  16. Let omega be the complex number cos((2pi)/3)+isin((2pi)/3). Then the...

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  17. If alpha and beta are the roots of the equation x^(2)-x+1=0, alpha^(20...

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  18. The number of complex numbers z such that |z-1|=|z+1|=|z-i| is

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  19. If z is any complex number satisfying abs(z-3-2i) le 2, where i=sqrt(-...

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  20. The set {R e((2i z)/(1-z^2)): zi sacom p l e xnu m b e r ,|z|=1,z=+-1}...

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