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If z(barz+3)=2 then the locus of z = x +...

If `z(barz+3)=2` 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) + 2x - 4y = 0` such that `y lt 0 , x^(2) + y^(2) gt1`

D

`x^(2) + y^(2) + 2x - 4y = 0` such that `2x - y + 4 gt0`

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The correct Answer is:
A
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AAKASH SERIES-COMPLEX NUMBERS-EXERCISE -II
  1. If |z^(2) - 1| = |z|^(2) + 1 , then z lies on

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  2. If omega is a complex cube root of unity , then sum(k = 1)^(6) ( omega...

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  3. If z(barz+3)=2 then the locus of z = x + iy is

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  4. If alpha + ibeta = tan^(-1) (z) , z = x +iy and alpha is constant then...

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  5. If (z - i)/(z +1) is purely imaginary then the locus of z = x +iy is

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  6. If log (tan 30^(@)) ( (2 |z|^(2) + 2 |z| - 3)/(|z| + 1)) lt -2 , then

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  7. The locus of z satisfying the inequality log ((1)/(3)) |z + 1| gt log(...

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  8. If z(1) = 8 + 4i , z(2) = 6 + 4i and z be a complex number such that ...

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  9. The triangle formed by the points 1 , (1 +i)/(sqrt2) and ias vertices ...

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  10. If |z| =3 , the area of the triangle whose sides are z , omega z and ...

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  11. Let z(1) , z(2) be two roots of the equation z^(2) + az + b = 0 , z be...

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  12. In Argand diagram , O , P , Q represent the origin , z and z +iz resp...

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  13. If a is a complex number and b is a real number then the equation bar...

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  14. The complex numbers z(1) , z(2) and z(3) satisfying (z(1) - z(3))/(z(2...

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  15. The cube roots of unity in an Argand plane represent the vertices of a...

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  16. Let z(1) and z(2) be two non-zero complex numbers such that (z(1))/(z(...

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  17. Let the complex number z(1) , z(2) , z(3) be the vertices of an equila...

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  18. Log (log i) =

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  19. The value of i^(i^(-i…..oo)) = x + iy then x^(2) + y^(2) =

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  20. The real and imaginary parts of log (1 + i) =

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