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If Arg ((z+1)/(z-1))=pi/6 then the locu...

If Arg `((z+1)/(z-1))=pi/6` then the locus of z = x + iy is

A

`x^(2) + y^(2) + 3x - 2 = 0 , y = 0`

B

`x = 0` such that `y gt (2)/(3)`

C

`x^(2) + y^(2) + 2 sqrt3 y - 1 = 0` such that `y lt 0 , x^(2) + y^(2) gt 1`

D

`x^(2) + y^(2) + 2x - 4y = 0` such that `2x - y + 4 gt 0`

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The correct Answer is:
C
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AAKASH SERIES-COMPLEX NUMBERS-PRACTICE EXERCISE
  1. If (sqrt3 + i) = (a + ib) (c + id) then tan^(-1) (b)/(a) + tan^(-1) (d...

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  2. Let z,w be complex number such that barz+ibarw=0 and arg zw =pi . Then...

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  3. If Arg ((z+1)/(z-1))=pi/6 then the locus of z = x + iy is

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  4. If |z| = 1 and arg [z^(2) + barz] = x arg z then x

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  5. If z = x + iy and if the point P in the Argand plane represents z , th...

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  6. If |z-3+i| = 4 then the locus of z = x +iy is

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  7. If |(z-1)/(z-3)| = 2 then the locus of z = x +iy is

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  8. The locus of the point z = x +iy satisfying the equation |(z-1)/(z+1)|...

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  9. The equation of the locus of 2 such that |(z-i)/(z+i)|=2, where z = x ...

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  10. The locus of the point z in the argrand plane for which |z+1|^2+|z-1|^...

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  11. If |z+i|^2-|z-i|^2=3 then the locus of z is

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  12. The points representing the complex numbers z for which |z+4|^2-|z-4|^...

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

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  14. If |z(1) | = |z(2)| = 1 , then |z(1) + z(2)| =

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  15. The modulus of sqrt2i-sqrt(-2i) is

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  16. If |z-1| = 2 then the locus of z is

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  17. If |z + 1| = sqrt2 | z- 1| and z is a complex number , then the locus ...

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  18. If the complex numbers z(1) , z(2) , z(3) represents the vertices of a...

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  19. If z = 2e^(i"" (pi)/(4)) then |e^(iz)| =

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  20. If |z + barz| + |z - barz| , then the locus of z is

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