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If Amp ((z+2)/(z-4i))=pi/2 then the loc...

If Amp `((z+2)/(z-4i))=pi/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) gt 1`

D

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

Text Solution

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The correct Answer is:
D
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AAKASH SERIES-COMPLEX NUMBERS-EXERCISE -II
  1. If the imaginary part of (2z + 1)/(iz+ 1) is -2 , then the locus of th...

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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  18. I: The modulus of (sqrt3 + i)/((1 + i) (1 + sqrt3i)) is (1)/(sqrt2) ...

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  19. I: If a and b are positive real numbers then sqrt(-a) xx sqrt(-b) = -s...

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  20. I : The number of solutions of the equation z^(2) + |z|^(2) = 0 is 2 ...

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