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`z_1, z_2, z_3,z_4` are distinct complex numbers representing the vertices of a quadrilateral `A B C D` taken in order. If `z_1-z_4=z_2-z_3 and "arg"[(z_4-z_1)//(z_2-z_1)]=pi//2` , the quadrilateral is

A

Rhombus

B

Square

C

Rectangle

D

A cyclic quadrilateral

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The correct Answer is:
C, D
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AAKASH INSTITUTE ENGLISH-COMPLEX NUMBERS AND QUADRATIC EQUATIONS-Assignment (Section -C) (objective Type Questions ( more thena one options are correct )
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  2. If z(1+a)=b+i ca n da^2+b^2+c^2=1, then [(1+i z)//(1-i z)= (a+i b)/(1...

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  3. z1, z2, z3,z4 are distinct complex numbers representing the vertices o...

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  4. If alpha , beta , gamma are cube roots of p lt 0, then for any x , y,...

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  5. If z is a complex number satisfying z + z^-1 = 1 then z^n + z^-n , n i...

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  6. If z satisfies |z-1| lt |z +3| " then " omega = 2 z + 3 -i satisfies

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  7. If |z + omega|^(2) = |z|^(2)+|omega|^(2), where z and omega are co...

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  8. Let z(1)and z(2)be two complex numbers represented by points on circle...

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  9. Let complex number z satisfy |z - 2/z| =1 " then " |z| can take all v...

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  10. If z=x+i y , then the equation |(2z-i)/(z+1)|=m does not represents a ...

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  11. If root3(-1) = -1 , -omega, -omega^(2) , then roots of the equation ...

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  12. If z(1)=p+iq and z(2) = u = iv are complex numbers such that |z(1)|=...

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  13. The pressure-volume of various thermodynamic process is shown in graph...

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  14. If z(1) ,z(2) be two complex numbers satisfying the equation |(z(1)...

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  15. If sin alpha, cosalpha are the roots of the equation x^2 + bx + c = 0 ...

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  16. If alpha, beta are the roots of the equation ax^(2) +2bx +c =0 and a...

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  17. The solution set of the inequality (x+3)^(5) -(x -1)^(5) ge 244 is

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  18. Let a,b,c be real numbers in G.P. such that a and c are positive , the...

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  19. Let cos alpha be a root of the equation 25x^(2) +5x -12 = 0 -1 lt x...

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  20. If the quadratic equations x^(2) +pqx +r=0 and z^(2) +prx +q=0 have a...

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