Home
Class 11
MATHS
If a ,b ,c are non zero complex numbers ...

If `a ,b ,c` are non zero complex numbers of equal modlus and satisfy `a z^2+b z+c=0,` hen prove that `(sqrt(5)-1)//2lt=|z|lt=(sqrt(5)+1)//2.`

Promotional Banner

Topper's Solved these Questions

  • BINOMIAL THEOREM

    CENGAGE PUBLICATION|Exercise All Questions|363 Videos
  • CONIC SECTIONS

    CENGAGE PUBLICATION|Exercise All Questions|1167 Videos

Similar Questions

Explore conceptually related problems

Find the non-zero complex number z satisfying z =i z^2dot

Let a ,b and c be any three nonzero complex number. If |z|=1 and' z ' satisfies the equation a z^2+b z+c=0, prove that a .bar a = c .bar c and |a||b|= sqrt(a c( bar b )^2)

Find the complex number z satisfying R e(z^2) =0,|z|=sqrt(3.)

If z_1 and z_2 are non zero complex numbers such that abs(z_1-z_2)=absz_1+absz_2 then

If z_1 and z_2 be two non-zero complex numbers such that |z_1+z_2|=|z_1|+|z_2| ,then prove that argz_1-argz_2=0 .

Find the conjugate of the complex number z=sqrt5-2i

If |z-4| lt |z-2|, where z is a complex number, then its solution is-

The complex number z satisfying the equation |z-i|=|z+1|=1 is

if z_1 and z_2 are two complex numbers such that absz_1lt1ltabsz_2 then prove that abs(1-z_1barz_2)/abs(z_1-z_2)lt1

Modulus of non zero complex number z satisfying barz +z=0 and |z|^2-4z i=z^2 is _________.

CENGAGE PUBLICATION-COMPLEX NUMBERS AND QUADRATIC EQUATIONS-All Questions
  1. Match the following for the equation x^2+a|x|+1=0,w h e r ea is a para...

    Text Solution

    |

  2. Find the ordered pair (x ,y) for which x^2-y^2-i(2x+y)=2idot

    Text Solution

    |

  3. If a ,b ,c are non zero complex numbers of equal modlus and satisfy a ...

    Text Solution

    |

  4. Let z be not a real number such that (1+z+z^2)//(1-z+z^2) in R , then...

    Text Solution

    |

  5. Let a is a real number satisfying a^3+1/(a^3)=18 . Then the value of a...

    Text Solution

    |

  6. Find non zero integral solutions of |1-i|^x=2^xdot

    Text Solution

    |

  7. Column I, Column II If x^2+a x+b=0 has roots alpha,betaa n dx^2+p x+...

    Text Solution

    |

  8. If (1+i)(1+2i)(1+3i)......(1+n i)=(x+i y) , show that 2. 5. 10...... (...

    Text Solution

    |

  9. If a x^2+b x+c=0,a ,b ,c in R has no real zeros, and if c<0 , then wh...

    Text Solution

    |

  10. If omega is a cube root of unity, then find the value of the following...

    Text Solution

    |

  11. If f(x)=sqrt(x^2+a x+4) is defined for all x , then find the value of ...

    Text Solution

    |

  12. If omega is a cube root of unity, then find the value of the following...

    Text Solution

    |

  13. Find the domain and range of f(x)=sqrt(x^2-4x+6)

    Text Solution

    |

  14. Prove that |z1+z2|^2=|z1|^2+|z2|^2, ifz1//z2 is purely imaginary.

    Text Solution

    |

  15. Find the range of the function f(x)=6^x+3^x+6^(-x)+e^(-x)+2.

    Text Solution

    |

  16. If omega is a cube root of unity, then find the value of the following...

    Text Solution

    |

  17. If alpha ,beta are the roots of the equation 2x^2+2(a+b)x+a^2+b^2=0 th...

    Text Solution

    |

  18. Let z1,z2, z3,......, zn be complex numbers such that |z1|=|z2|=...=|z...

    Text Solution

    |

  19. If a ,b , in R such that a+b=1a n d(1-2ab)(a^3+b^3)=12 . The value ...

    Text Solution

    |

  20. If |z|lt=4 , then find the maximum value of |i z+3-4i|dot

    Text Solution

    |