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If |z1|=|z2|=|z3|=1 then value of |z1-z3...

If `|z_1|=|z_2|=|z_3|=1` then value of `|z_1-z_3|^2+|z_3-z_1|^2+|z_1-z_2|^2` cannot exceed

A

3

B

6

C

9

D

12

Text Solution

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The correct Answer is:
C
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MCGROW HILL PUBLICATION-COMPLEX NUMBERS -EXERCISE LEVEL 1
  1. If |z1|=|z2|=|z3|=1 are twu complex numbers such that |z1|=|z2|=sqrt2...

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  2. Let z(1), z(2), z(3) be three non-zero complex numbers such that z(1) ...

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  3. If |z1|=|z2|=|z3|=1 then value of |z1-z3|^2+|z3-z1|^2+|z1-z2|^2 cannot...

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  4. Let z1z2,z3, be three complex number such that z1+z2+z3=0 and |...

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  5. Let z(1), z(2), z(3) be three complex numbers such that |z(1)| = |z(2)...

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  6. Suppose z is a complex number such that z ne -1, |z| = 1, and arg(z) =...

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  7. Let a = Im((1+z^(2))/(2iz)), where z is any non-zero complex number. T...

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  8. Number of complex numbers such that |z| = 1 and z = 1 - 2 bar(z) is

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  9. Let z(1), z(2) be two complex numbers such that z(1) ne 0 and z(2)//z(...

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  10. If z = i(1+sqrt(3)),"then"z^(4)+2z^(3)+4z^(2) + 5 is equal to

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  11. If the fourth roots of unity are z1, z2, z3, z4 and z1^2+z2^2+z3^2+z4^...

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  12. Suppose arg (z) = - 5 pi//13, then arg((z + bar(z))/(1+z bar(z))) is

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  13. The number of values of theta in (0, pi], such that (cos theta + i sin...

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  14. If z in C - {0, -2} is such that log((1//7)) |z-2| gt log((1//7)) |z| ...

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  15. Im ((2z+1)/(iz+1))=5 represents

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  16. If z1,z2 are two complex numbers such that Im(z1+z2)=0,Im(z1z2)=0, the...

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  17. The number (1+ i)^n / (1 - i )^(n-2) is equal to

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  18. Let omega ne 1, be a cube root of unity, and f : I rarr C be defined b...

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  19. If z + (1)/(z) = 2 cos theta, z in "C then z"^(2n) - 2z^(n) cos (n the...

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  20. If omega ne 1 is a cube root of unity, then z=sum(k=1)^(60)omega^(k) -...

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