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If z + z^(-1)= 1, then find the value of...

If `z + z^(-1)= 1`, then find the value of `z^(100) + z^(-100)`.

A

i

B

`-i`

C

1

D

`-1`

Text Solution

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The correct Answer is:
d
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OBJECTIVE RD SHARMA-COMPLEX NUMBERS -Exercise
  1. The general value of theta which satisfies the equation (costheta+isin...

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  2. If z is a complex numbers such that z ne 0 and "Re"(z)=0, then

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  3. If z + z^(-1)= 1, then find the value of z^(100) + z^(-100).

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  4. Let A,B and C represent the complex number z1, z2, z3 respectively on ...

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  5. Number of solutions of the equation z^(2)+|z|^(2)=0, where z in C, is

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  6. The number of solutions of the equation z^2+z=0 where z is a a complex...

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  7. The centre of a square is at the origin and one of the vertex is 1-i e...

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  8. Let za n domega be two complex numbers such that |z|lt=1,|omega|lt=1a ...

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  9. The system of equation |z+1+i|=sqrt2 and |z|=3}, (where i=sqrt-1) ha...

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  10. The triangle with vertices at the point z1z2,(1-i)z1+i z2 is

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  11. Let alpha and beta be two fixed non-zero complex numbers and 'z' a var...

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  12. The center of a square is at z=0. A is z(1), then the centroid of the ...

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  13. If z=x+i y , then he equation |(2z-i)//(z+1)|=m represents a circle, t...

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  14. If x^2-2xcos theta+1=0, then the value of x^(2n)-2x^n cosntheta+1, n ...

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  15. If p^(2)-p+1=0, then the value of p^(3n) can be

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  16. If n in Z, then (2^(n))/(1+i)^(2n)+(1+i)^(2n)/(2^(n)) is equal to

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  17. If arg (z(1)z(2))=0 and |z(1)|=|z(2)|=1, then

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

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

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

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