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If |z -1| lt 2 |z - 2| then the locus of...

If `|z -1| lt 2 |z - 2|` then the locus of `z = x + iy` is

A

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

B

`3x^(2) + 3y^(2) - 14 x + 15 gt 0`

C

`3x^(2) + 3y^(2) - 14 x + 15 lt 0`

D

`3x^(2) + 3y^(2) - 14 x + 15 = 0`

Text Solution

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The correct Answer is:
B
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AAKASH SERIES-COMPLEX NUMBERS-EXERCISE -II
  1. The region of the argand plane defined by |z-i| + |z +i| le 4 is

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  2. If (z+2)/(z+6i) is purely real then the locus of z = x +iy is

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  3. If |z -1| lt 2 |z - 2| then the locus of z = x + iy is

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  4. If the imaginary part of (2z + 1)/(iz+ 1) is -2 , then the locus of th...

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  5. z = x + iy and w = (1 - iz)/(z-i) , then |w| = 1 implies in the comple...

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  6. If Amp ((z+2)/(z-4i))=pi/2 then the locus of z = x + iy is .

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  7. If Arg ((2 - z)/(2 + z)) = (pi)/(6) and z = x + iy , then the locus of...

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  8. If omega=z/(z-1/3i) and |omega|=1 then z lies on

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  9. The points in the set {zinC: Arg " ((z-2)/(Z-6i))=pi/2} lie on the cu...

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  10. Statement - I : If n = 4m + 3 , is integer then i^(n) is equal to -i ...

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  11. The complex equation |z + 1- i| = |z + i-1| represents a

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  12. If z(1) = 1 , z(2) = i and A = Arg (z(1) z(2)) B = Arg ((z(1))/(z(2)...

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  13. The descending order of the principal values of arguments of the compl...

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  14. If x(n) + iy(n) = (1 + i)^(n) then x(n - 1) y(n) - x(n) y(n- 1) =

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  15. If x=-5+4i then x^4+9x^3+35x^2-x+4=

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  16. If x is a fifth root of unity then 1 + x + x^(2) + …x^(100)

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  17. If omega = sqrt(z^(2) - 1) where omega is a cube root of unity and z =...

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  18. If x(n) = omega^(n) + (1)/(omega^(n)) then x(1) x(2) x(3)…, x(12) =

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  19. If three complex number are in A.P then they lie on

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  20. The maximum value of |3z + 9 - 7i| if |z + 2- i| = 5 is

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