Home
Class 12
MATHS
Find the range of real number alpha f...

Find the range of real number `alpha ` for which the equation `z + alpha |z-1| + 2i= 0`

A

`[-(sqrt(5))/(2),(sqrt(5))/(2)]`

B

`[-(sqrt(3))/(2),(sqrt(3))/(2)]`

C

`[0,(sqrt(5))/(2)]`

D

`(-oo,-(sqrt5)/(2))uu[(sqrt5)/(2),oo]`

Text Solution

Verified by Experts

The correct Answer is:
A
Promotional Banner

Topper's Solved these Questions

  • COMPLEX NUMBERS

    VMC MODULES ENGLISH|Exercise NUMRICAL VALUE TYPE FOR JEE MAIN|14 Videos

  • COMPLEX NUMBERS

    VMC MODULES ENGLISH|Exercise JEE ARCHIVE|76 Videos

  • COMPLEX NUMBERS

    VMC MODULES ENGLISH|Exercise LEVEL - 1|90 Videos

  • CIRCLES

    VMC MODULES ENGLISH|Exercise JEE ADVANCED ( ARCHIVE )|68 Videos

  • CONIC SECTIONS

    VMC MODULES ENGLISH|Exercise JEE ADVANCED ARCHIVE|76 Videos

Similar Questions

Explore conceptually related problems

Find the range of real number alpha for which the equation z+alpha|z-1|+2i=0 has a solution.

Find the range of real number alpha for which the equation z+alpha|z-1|+2i=0 has a solution.

Find the range of K for which the equation |z+i| - |z-i | = K represents a hyperbola.

The number of values of alpha in [-10pi, 10pi] for which the equations (sin alpha)x-(cos alpha)y+3z=0, (cos alpha)x+(sin alpha)y-2z=0 and 2x+3y+(cos alpha)z=0 have nontrivial solution is

Find the number of complex numbers which satisfies both the equations |z-1-i|=sqrt(2)a n d|z+1+i|=2.

The value of |alpha| for which the system of equation alphax+y+z=alpha-1 x+alphay+z=alpha-1 x+y+alphaz=alpha-1 has no solution , is "____"

The value of |alpha| for which the system of equation alphax+y+z=alpha-1 x+alphay+z=alpha-1 x+y+alphaz=alpha-1 has no solution , is "____"

The value of |alpha| for which the system of equation alphax+y+z=alpha-1 x+alphay+z=alpha-1 x+y+alphaz=alpha-1 has no solutions, is ________.

The real value of alpha for which the expression (1- isin alpha)/(1+2i sinalpha) is purely real is

Let lambda and alpha be real. Then the numbers of intergral values lambda for which the system of linear equations lambdax +(sin alpha) y+ (cos alpha) z=0 x + (cos alpha) y+ (sin alpha) z=0 -x+(sin alpha) y -(cos alpha) z=0 has non-trivial solutions is

VMC MODULES ENGLISH-COMPLEX NUMBERS -LEVEL - 2
  1. For |z-1|=1, show that tan{[a r g(z-1)]//2}-(2i//z)=-idot

    Text Solution

    |

  2. If nge3and1,alpha(1),alpha(2),.......,alpha(n-1) are nth roots of unit...

    Text Solution

    |

  3. Let |z|=2and w=(z+1)/(z-1),where z ,w , in C (where C is the set of c...

    Text Solution

    |

  4. If z=x+i y is a complex number with x ,y in Qa n d|z|=1, then show th...

    Text Solution

    |

  5. If z^3+(3+2i)z+(-1+i a)=0 has one real roots, then the value of a lies...

    Text Solution

    |

  6. Given z=f(x)+ig(x) where f,g:(0,1) to (0,1) are real valued functions....

    Text Solution

    |

  7. Let z1a n dz2 be complex numbers such that z1!=z2 and |z1|=|z2|dot If ...

    Text Solution

    |

  8. If m and x are two real number s and i=sqrt(-1), prove that e^(2mico...

    Text Solution

    |

  9. Find the range of real number alpha for which the equation z + al...

    Text Solution

    |

  10. The condition that x^(n+1)-x^(n)+1 shall be divisible by x^(2)-x+1 is ...

    Text Solution

    |

  11. Find the point of intersection of the curves a r g(z-3i)=(3pi)/4a n d ...

    Text Solution

    |

  12. If the equation z^4+a1z^3+a2z^2+a3z+a4=0 where a1,a2,a3,a4 are real co...

    Text Solution

    |

  13. The value of the expression 2(1+(1)/(omega))(1+(1)/(omega^(2)))+3(2+(1...

    Text Solution

    |

  14. If z=ilog(e)(2-sqrt(3)),"where"i=sqrt(-1) then the cos z is equal to

    Text Solution

    |

  15. If z satisfies |z+1| lt |z-2|, then w=3z+2+i

    Text Solution

    |

  16. For any two complex numbers z1\ a n d\ z2 and any two real numbers a ,...

    Text Solution

    |

  17. If w=cos""(pi)/(n)+isin""(pi)/(n) then value of 1+w+w^(2)+.......+w^(n...

    Text Solution

    |

  18. Find the sum 1xx(2-omega)xx(2-omega^(2))+2xx(-3-omega)xx(3-omega^(2))+...

    Text Solution

    |

  19. If (1+x+x^2)^n = a0+a1x+a2x2 +..............+a(2n)x^(2n) then the valu...

    Text Solution

    |

  20. If 1,alpha,alpha^(2),.......,alpha^(n-1) are the n^(th) roots of unity...

    Text Solution

    |