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If `z_1, z_2, z_3, z_4` are the four complex numbers represented by the vertices of a quadrilateral taken in order such that `z_1-z_4 = z_2-z_3` and `"amp" (z_4-z_1)/(z_2-z_1) = pi/2` then the quadrilateral is a

A

a rhombus

B

a square

C

a rectangle

D

not a cyclic quadrilateral

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The correct Answer is:
c
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OBJECTIVE RD SHARMA-COMPLEX NUMBERS -Chapter Test
  1. If z(bar(z+alpha))+barz(z+alpha)=0, where alpha is a complex constant,...

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  2. Let A,B,C be three collinear points which are such that AB.AC=1 and th...

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  3. If z1, z2, z3, z4 are the four complex numbers represented by the vert...

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  4. If z be a complex number, then |z-3-4i|^(2)+|z+4+2i|^(2)=k represent...

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  5. In Argand diagram, O, P, Q represent the origin, z and z+ iz respectiv...

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  6. If (2z(1))/(3z(2)) is purely imaginary number, then |(z(1)-z(2))/(z(1)...

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  7. If omega is a cube root of unity then find the value of sin((omega^(10...

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  8. If center of a regular hexagon is at the origin and one of the vertice...

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  9. If z^(2)+(p+iq)z+(r+is)=0, where,p,q,r,s are non-zero, has real roots...

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  10. Let z1, z2, z3 be three vertices of an equilateral triangle circumscri...

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  11. If omega is the complex cube root of unity, then the value of omega+om...

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  12. the locus of z=i+2exp(i(theta+pi/4)) is

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  13. If z lies on the circle |z-1|=1, then (z-2)/z is

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  14. If a gt 0 and the equation |z-a^(2)|+|z-2a|=3, represents an ellipse, ...

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  15. For any complex number z , find the minimum value of |z|+|z-2i|dot

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  16. Find the greatest and the least value of |z1+z2| ifz1=24+7ia n d|z2|=6...

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  17. For all complex numbers z1, z2 satisfying |z1| =12 and |z2-3-4i|=5, ...

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  18. If k gt 1, |z(1)| lt k and |(k-z(1)barz(2))/(z(1)-kz(2))|=1, then

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  19. If |z-i|=1 and arg (z) =theta where 0 lt theta lt pi/2, then cottheta-...

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  20. If Re(z)<0 then the value of (1+z+z^2+.....+z^n) cannot exceed

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