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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

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-COMPLEX NUMBERS AND QUADRATIC EQUATIONS-Assignment (Section -C) (objective Type Questions ( more thena one options are correct )
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  2. lf a, b, c are real numbers and z is a complex number such that, a^2+b...

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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 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 z1, z2 be two complex numbers represented by points on the 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 he equation |(2z-i)//(z+1)|=m represents a circle, t...

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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) = a + ib " and " z(2) + c id are complex numbers such that ...

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  13. If log(1/2)((|z|^2+2|z|+4)/(2|z|^2+1))<0 then the region traced by z ...

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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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