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If the points z(1),z(2),z(3) are the ver...

If the points `z_(1),z_(2),z_(3)` are the vertices of an equilateral triangle in the Argand plane, then which one of the following is not correct?

A

`1/(z_(1)-z_(2))+1/(z_(2)-z_(3))+1/(z_(3)-z_(1))=0`

B

`z_(1)^(2)+z_(2)^(2)+z_(3)^(2)=z_(1)z_(2)+z_(2)z_(3)+z_(3)z_(1)`

C

`(z_(1)-z_(2))^(2)+(z_(2)-z_(3))^(2)+(z_(3)-z_(1))^(2)=0`

D

`z_(1)^(3)+z_(2)^(3)+z_(3)^(3)+3z_(1)z_(2)z_(3)=0`

Text Solution

Verified by Experts

The correct Answer is:
d
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OBJECTIVE RD SHARMA ENGLISH-COMPLEX NUMBERS -Exercise
  1. Given z is a complex number with modulus 1. Then the equation [(1+i a)...

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  2. The center of a regular polygon of n sides is located at the point z=0...

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  3. If the points z(1),z(2),z(3) are the vertices of an equilateral triang...

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  4. For any complex number z, the minimum value of |z|+|z-1|

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  5. The inequality |z-4| < |z-2| represents

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  6. Find the number of non-zero integral solutions of the equation |1-i|^(...

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  7. If "Im"(2z+1)/(iz+1)=-2, then locus of z, is

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  8. about to only mathematics

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  9. If x=-5+2sqrt(-4) , find the value of x^4+9x^3+35 x^2-x+4.

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  10. If z(1),z(2), z(3) are vertices of an equilateral triangle with z(0) i...

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  11. If z(1) , z(2) are two complex numbers such that I m (z(1) + z(2)) = 0...

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  12. If z^2+z|z|+|z^2|=0, then the locus z is a. a circle b. a straight ...

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  13. If log(sqrt3) ((|z|^(2)-|z|+1)/(2+|z|)) lt 2 ,then the locus of z is

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  14. Let g(x) and h(x) are two polynomials such that the polynomial P(x) =g...

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  15. If g(x) and h(x) are two polynomials such that the polynomials P(x)=g(...

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  16. if x(k) = cos pi/3^(k) + isin pi/3^(k) , find x(1)x(2)x(3)……oo (...

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  17. If (a1+ib1)(a2+ib2).....(an+ibn)=A+iB, then (a1^2+b1^2)(a2^2+b2^2).......

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  18. If (a(1)+ib(1))(a(2)+ib(2))………………(a(n)+ib(n))=A+iB, then sum(i=1)^(n) ...

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  19. If cosalpha+2cosbeta+3cosgamma=sinalpha+2sinbeta+3singamma=0,t h e nt ...

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  20. If alpha,betaandgamma are the cube roots of P(p)lt0), then for any x, ...

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