Home
Class 11
MATHS
Let z and omega be two complex numbers ...

Let `z` and `omega` be two complex numbers such that `|z|lt=1,|omega|lt=1` and `|z-iomega|=|z-i bar omega|=2,` then `z` equals (a)`1ori` (b). `ior-i` (c). `1or-1` (d). `ior-1`

Text Solution

AI Generated Solution

Promotional Banner

Topper's Solved these Questions

  • BINOMIAL THEOREM

    CENGAGE ENGLISH|Exercise All Questions|365 Videos
  • CONIC SECTIONS

    CENGAGE ENGLISH|Exercise All Questions|1344 Videos

Similar Questions

Explore conceptually related problems

If z and omega are two non-zero complex numbers such that |zomega|=1 and arg(z)-arg(omega)=pi/2 , then barzomega is equal to

Let z and omega be two non-zero complex numbers, such that |z|=|omega| and "arg"(z)+"arg"(omega)=pi . Then, z equals

Let Z and w be two complex number such that |zw|=1 and arg(z)−arg(w)=pi//2 then

The number of complex numbers z such that |z-1|=|z+1|=|z-i| is

Let z and omega be two non zero complex numbers such that |z|=|omega| and argz+argomega=pi , then z equals (A) omega (B) -omega (C) baromega (D) -baromega

Let z and omega be two non zero complex numbers such that |z|=|omega| and argz+argomega=pi, then z equals (A) omega (B) -omega (C) baromega (D) -baromega

Let z and w be two nonzero complex numbers such that |z|=|w| and arg(z)+a r g(w)=pidot Then prove that z=- barw dot

If z and w are two complex number such that |z w|=1 and a rg(z)-a rg(w)=pi/2 , then show that barz w=-i

Suppose z and omega are two complex number such that |z + iomega| = 2 . Which of the following is ture about |z| and |omega| ?

Let z be a complex number such that |z|+z=3+I (Where i=sqrt(-1)) Then ,|z| is equal to

CENGAGE ENGLISH-COMPLEX NUMBERS AND QUADRATIC EQUATIONS-All Questions
  1. The interval of a for which the equation t a n^2x-(a-4)tanx+4-2a=0 has...

    Text Solution

    |

  2. The range of a for which the equation x^2+ax-4=0 has its smaller root ...

    Text Solution

    |

  3. Let z and omega be two complex numbers such that |z|lt=1,|omega|lt=1 ...

    Text Solution

    |

  4. Consider the equation x^2+2x-n=0 where n in N and n in [5,100] The t...

    Text Solution

    |

  5. If n1, n2 are positive integers, then (1 + i)^(n1) + ( 1 + i^3)^(n1) +...

    Text Solution

    |

  6. The total number of values a so that x^2-x-a=0 has integral roots, wh...

    Text Solution

    |

  7. If i=sqrt-1, then 4+5(-1/2+(isqrt3)/2)^334+3(-1/2+(isqrt3)/2)^365 is e...

    Text Solution

    |

  8. Let P(x)=x^3-8x^2+c x-d be a polynomial with real coefficients and wi...

    Text Solution

    |

  9. If a r g(z)<0, then a r g(-z)-"a r g"(z) equals pi (b) -pi (d) -pi/2...

    Text Solution

    |

  10. Let P(x)=5/3-6x-9x^2a n dQ(y)=-4y^2+4y+(13)/2dot if there exists uniq...

    Text Solution

    |

  11. If z1,z2, z3 are complex numbers such that |z1|=|z2|=|z3|=|1/z1+1/z2+1...

    Text Solution

    |

  12. if a lt c lt b, then check the nature of roots of the equation (a ...

    Text Solution

    |

  13. Q. Let z1 and z2 be nth roots of unity which subtend a right angle at...

    Text Solution

    |

  14. If a+b+c=0 then check the nature of roots of the equation 4a x^2+3b x+...

    Text Solution

    |

  15. The complex numbers z1, z2 and z3 satisfying (z1-z3)/(z2-z3) =(1- i sq...

    Text Solution

    |

  16. Find the value of a for which the sum of the squares of the roots of t...

    Text Solution

    |

  17. For all complex numbers z1,z2 satisfying |z1|=12 and |z2-3-4i|=5, fin...

    Text Solution

    |

  18. If x1, a n dx2 are the roots of x^2+(sintheta-1)x-1/2(cos^2theta)=0, ...

    Text Solution

    |

  19. If y="sec"(tan^(-1)x),t h e n(dy)/(dx)a tx=1 is (a)cospi/4 (b) sinp...

    Text Solution

    |

  20. If p ,q in {1,2,3,4,5} , then find the number of equations of form p^2...

    Text Solution

    |