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If Zr=cos((2rpi)/5)+isin((2rpi)/5),r=0,1...

If `Z_r=cos((2rpi)/5)+isin((2rpi)/5),r=0,1,2,3,4,...` then `z_1z_2z_3z_4z_5` is equal to

A

`-1`

B

0

C

1

D

none of these

Text Solution

Verified by Experts

The correct Answer is:
C
Clearly, `z_(0),z_(1),z_(3),z_(4)` are fifth roots of unity. We know that the product of `n^(6th)` roots of unity is `(-1)^(n-1)`.
`therefore z_(0)z_(1)z_(2)z_(3)z_(4) = (-1)^(5-1)=1`
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OBJECTIVE RD SHARMA-COMPLEX NUMBERS -Section I - Solved Mcqs
  1. If omega is an imaginary cube root of unity, then find the value of (1...

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  2. If alpha is a non-real fifth root of unity, then the value of 3^(|1+a...

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  3. If Zr=cos((2rpi)/5)+isin((2rpi)/5),r=0,1,2,3,4,... then z1z2z3z4z5 is...

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  4. z is a complex number satisfying z^(4)+z^(3)+2z^(2)+z+1=0, then |z| is...

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  5. if (5z2)/(7z1) is purely imaginary number then |(2z1+3z2)/(2z1-3z2) |...

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  6. The locus of point z satisfying R e(1/z)=k ,w h e r ek is a nonzero re...

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  7. If z lies on the circle I z l = 1, then 2/z lies on

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  8. The maximum value of |z| where z satisfies the condition |z+(2/z)|=2 i...

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  9. If |z-4/z|=2 , then the maximum value of |Z| is equal to (1) sqrt(3...

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  10. if |z^2-1|=|z|^2+1 then z lies on

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  11. If the number (z-1)/(z+1) is purely imaginary, then

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  12. If |z|=k and omega=(z-k)/(z+k), then Re(omega)=

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  13. If k>0, |z|=|w|=k, and alpha=(z-bar(w))/(k^2+zbar(w)), Re(alpha)

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  14. The region in the Argand diagram defined by |z-2i|+|z+2i| lt 5 is the ...

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  15. Prove that |Z-Z1|^2+|Z-Z2|^2=a will represent a real circle [with cent...

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  16. The equation |z-1|^(2)+|z+1|^(2)=2, represent

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  17. The points representing the complex numbers z for which |z+4|^(2)-|z-4...

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  18. If |z+barz|=|z-barz|, then value of locus of z is

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  19. If |z+barz|+|z-barz|=2, then z lies on

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  20. The closest distance of the origin from a curve given as Abarz+barAz+A...

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