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If omega is the cube root of unity of th...

If `omega` is the cube root of unity of the equation `z^(3)=1`, then the value of : `(1)/(2)+(3)/(8)+(9)/(32)+(27)/(128)+.....`to `oo (omega)/(2)+omega^(2)` is

A

-1

B

1

C

-i

D

i

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A
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HIMALAYA PUBLICATION-COMPLEX NUMBERS-QUESTION BANK
  1. If x=a+b, y=a omega+b omega^(2), z=a omega^(2)+b omega, then x y z=

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  2. The argument of (1-i sqrt(3))/(1+i sqrt(3))=

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  3. If omega is the cube root of unity of the equation z^(3)=1, then the v...

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  4. The reciprocal of 3+i sqrt(7) is

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  5. If (cos theta+i sin theta) .(cos 2 theta+i sin 2 theta) ldots ldots(c...

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  6. If ((1+i sqrt(3))/(1-i sqrt(3)))^(n) is an integer, then n=

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  7. The value of (1+omega^(2)+2 omega)^(3 n)-(1+omega+2 omega^(2))^(3 n)=

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  8. The real value of thetafor which the expression is (1+icos theta)/(1...

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  9. Let z=x+ iy then z . bar(z)=0 if and only if

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  10. (3+2 i sin theta)/(1-2 i sin theta) will be purely imaginary, if theta...

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  11. If the cube root of unity are 1,omega,omega^(2), then the roots of the...

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  12. If z is a complex number such that z=-bar(z) then

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  13. The complex number (1+2i)/(1-i) lies in

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  14. If P is the point in the Argand diagrma correspoinding to the complex ...

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  15. The smallest positive integral value of ' n ' such that [(1+sin (pi)...

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  16. The least positive integer n, for which ((1+i)^(n))/((1-i)^(n-2))is po...

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  17. If x+i y=(-1+i sqrt(3))^(2010), then x=

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  18. The value of |(1+i sqrt(3))/((1+(1)/(i+1))^(2))|=

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  19. If omega is an imaginary cube root of unity ,then the value of (1-omeg...

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  20. If P(x, y) denotes z=x+i y in Argand's plane and |(z-1)/(z+2 i)|=1, t...

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