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If z satisfies |z-1| lt |z +3| " then " ...

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

A

`|omega - 5 -i|lt | omega + 3+i|`

B

`|omega - 5| lt | omega +3|`

C

`lm (iomega) lt 1`

D

`|arg (omega -1) | lt pi/2`

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The correct Answer is:
B, D
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AAKASH INSTITUTE-COMPLEX NUMBERS AND QUADRATIC EQUATIONS-Assignment (Section -C) (objective Type Questions ( more thena one options are correct )
  1. If alpha , beta , gamma are cube roots of p lt 0, then for any x , y,...

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

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

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

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  5. Let z1, z2 be two complex numbers represented by points on the circle ...

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

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  7. If z=x+i y , then he equation |(2z-i)//(z+1)|=m represents a circle, t...

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

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  9. If z(1) = a + ib " and " z(2) + c id are complex numbers such that ...

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

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

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

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

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

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

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

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

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  18. The quadratic equation x^(2) - (m -3)x + m =0 has

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  19. If both roots of the equation x^(2) -2ax+a^(2)-1=0 lie between -3 and...

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  20. Let alpha, beta " the roots of " x^(2) -4x + A =0 and gamma, delta " ...

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