Home
Class 11
MATHS
If z is a complex number such that |z-1|...

If z is a complex number such that `|z-1|= |z+1|`, show that Re(z)= 0

Text Solution

AI Generated Solution

Promotional Banner

Topper's Solved these Questions

  • COMPLEX NUMBERS

    ICSE|Exercise Exercise (D)|20 Videos

  • COMPLEX NUMBERS

    ICSE|Exercise Exercise (E )|12 Videos

  • COMPLEX NUMBERS

    ICSE|Exercise Exercise (B)|69 Videos

  • COMPLEX NUMBER

    ICSE|Exercise MULTIPLE CHOICE QUESTIONS |34 Videos

  • COMPOUND AND MULTIPLE ANGLES

    ICSE|Exercise CHEPTER TEST |23 Videos

Similar Questions

Explore conceptually related problems

If z = x+iy is any complex number and |z-1| = |z+1| then show that |z| = y .

State true or false for the following. If z is a complex number such that z ne 0 " and Re " (z)= 0 " then Im" (z^(2)) = 0 .

If z_1 and z_2 are two complex numbers such that |\z_1|=|\z_2|+|z_1-z_2| show that Im (z_1/z_2)=0

If z_(1) = a + ib " and " z_(2) + c id are complex numbers such that |z_(1)| = |z_(2)| = 1 and Re (z_(1)bar (z)_(2)) = 0 , then the pair of complex numbers w_(1) = a + ic " and " w_(2) = b id satisfies :

Let z be a complex number such that |(z-5i)/(z+5i)|=1 , then show that z is purely real

If z_1=a + ib and z_2 = c + id are complex numbers such that |z_1|=|z_2|=1 and Re(z_1 bar z_2)=0 , then the pair ofcomplex nunmbers omega_1=a+ic and omega_2=b+id satisfies

If z is a complex number such that |z|>=2 then the minimum value of |z+1/2| is

z is a complex number such that |Re(z)| + |Im (z)| = 4 then |z| can't be

z is a complex number such that |Re(z)| + |Im (z)| = 4 then |z| can't be

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

ICSE-COMPLEX NUMBERS-Exercise (C)
  1. Find the modulus of (1-i)^(-2) + (1+ i)^(-2)

    Text Solution

    |

  2. If z= 6+8i, verify that |z|= |bar(z)|

    Text Solution

    |

  3. If z= 6+8i, verify that -|z| le " Re " (z) le |z|

    Text Solution

    |

  4. If z= 6+8i, verify that -|z| lt "Im" (z) lt |z|

    Text Solution

    |

  5. If z= 6+8i, verify that z^(-1)= (bar(z))/(|z|^(2))

    Text Solution

    |

  6. If z(1)=3 + 4i,z(2)= 8-15i, verify that |-z(1)| = |z(1)|

    Text Solution

    |

  7. If z(1)=3 + 4i,z(2)= 8-15i, verify that |z(1)^(2)| = |z(2)|^(2)

    Text Solution

    |

  8. If z(1)=3 + 4i,z(2)= 8-15i, verify that |z(1)z(2) |= |z(1)| |z(2)|

    Text Solution

    |

  9. If z(1)=3 + 4i,z(2)= 8-15i, verify that |(z(1))/(z(2))|= (|z(1)|)/(...

    Text Solution

    |

  10. If z(1)=3 + 4i,z(2)= 8-15i, verify that |z(1) + z(2)| lt |z(1)| + ...

    Text Solution

    |

  11. If z(1)=3 + 4i,z(2)= 8-15i, verify that |z(2)-z(1)| gt ||z(2)|- |z...

    Text Solution

    |

  12. If z(1)=3 + 4i,z(2)= 8-15i, verify that |z(1) + z(2)|^(2) + |z(1)-...

    Text Solution

    |

  13. Find the modulus of the following using the property of modulus (3+...

    Text Solution

    |

  14. Find the modulus of the following using the property of modulus (8+...

    Text Solution

    |

  15. Find the modulus of the following using the property of modulus (3+...

    Text Solution

    |

  16. Find the modulus of the following using the property of modulus ((2...

    Text Solution

    |

  17. Let z be a complex number such that |(z-5i)/(z+5i)|=1, then show that ...

    Text Solution

    |

  18. Find the complex number z satisfying the equation |(z-12)/(z-8i)|= (5)...

    Text Solution

    |

  19. If z is a complex number such that |z-1|= |z+1|, show that Re(z)= 0

    Text Solution

    |

  20. Solve |z|+z= 2+ i, where z is a complex number

    Text Solution

    |