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The complex numbers z1, z2 and z3 satisf...

The complex numbers `z_1, z_2 and z_3` satisfying `(z_1-z_3)/(z_2-z_3) =(1- i sqrt(3))/2` are the vertices of triangle which is (1) of area zero (2) right angled isosceles(3) equilateral (4) obtuse angled isosceles

A

Of area zero

B

Right angled isosceles

C

Equilateral

D

Obtuse angle isosceles

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Verified by Experts

The correct Answer is:
C
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AAKASH INSTITUTE ENGLISH-COMPLEX NUMBERS AND QUADRATIC EQUATIONS-Assignment (Section -B) (objective Type Questions ( one option is correct)
  1. The value of (i+sqrt3)^(100)+(i-sqrt3)^(100)+2^(100) is

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  2. Which of the following is not true ?

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  3. The complex numbers z1, z2 and z3 satisfying (z1-z3)/(z2-z3) =(1- i sq...

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  4. Let a=i^i and consider the following statements S1: a=e^(-pi/2), S2:T...

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  5. If z^(2)+z+1=0 then the value of (z+1/z)^(2)+(z^(2)+1/z^(2))^(2)+(z...

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  6. If omega is an imaginary fifth root of unity, then find the value of l...

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  7. If 1,alpha1,alpha2,alpha3,.........,alpha(3n) be the roots of the equt...

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  8. If z(1),z(2),z(3),z(4) are two pairs of conjugate complex numbers, th...

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  9. If |z-4 +3i| le 2 then the least and the greatest values of |z| are q

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  10. If |z1|=2,|z2|=3,|z3|=4 and |2z1+3z2+4z3|=4 then the expression |8z2z3...

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  11. If z1 = cos theta + i sin theta and 1,z1,(z1)^2,(z1)^3,.....,(z1)^(n-1...

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  12. The area of the triangle whose vertices are represented by the complex...

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

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  14. The value of (1-tan^(2)15^(@))/(1+tan^(2)15^(@)) is

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  15. Both the roots of the equation (x-b)(x-c)+(x-a)(x-c)+(x-a)(x-b)=0 are ...

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  16. If log sqrt(3)((|z|^(2)-|z|+1)/(2+|z|))gt2, then the locus of z is

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  17. If arg z = pi/4 ,then

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

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  19. The least value of p for which the two curves argz=pi/6 and |z-2sqrt(...

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  20. Re((z+4)/(2z-1)) = 1/2, then z is represented by a point lying on

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