Home
Class 11
MATHS
Let z be not a real number such that (1+...

Let `z` be not a real number such that `(1+z+z^2)//(1-z+z^2) in R ,` then prove tha `|z|=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_(1) and z_(2) are two complex numbers such that |z_(1)| lt 1 lt |z_(2)| , then prove that |(1- z_(1)barz_(2))//(z_(1)-z_(2))| lt 1

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

If z_1, z_2, z_3 are three complex numbers such that 5z_1-13 z_2+8z_3=0, then prove that [(z_1,(bar z )_1, 1),(z_2,(bar z )_2 ,1),(z_3,(bar z )_3 ,1)]=0

If z_1 and z_2 are two complex numbers such that |z_1|lt1lt|z_2| then prove that |(1-z_1barz_2)/(z_1-z_2)|lt1

Let z_(1),z_(2) be two complex numbers such that z_(1)+z_(2) and z_(1)z_(2) both are real, then

Let z_(1) and z_(2) be two given complex numbers such that z_(1)/z_(2) + z_(2)/z_(1)=1 and |z_(1)| =3 , " then " |z_(1)-z_(2)|^(2) is equal to

State true or false for the following. Let z_(1) " and " z_(2) be two complex numbers such that |z_(2) + z_(2)| = |z_(1) | + |z_(2)| , then arg (z_(1) - z_(2)) = 0

Fill in the blanks. If z_(1) " and " z_(2) are complex numbers such that z_(1) +z_(2) is a real number, then z_(1) = ….

If complex numbers z_(1)z_(2) and z_(3) are such that |z_(1)| = |z_(2)| = |z_(3)| , then prove that arg((z_(2))/(z_(1))) = arg ((z_(2) - z_(3))/(z_(1) - z_(3)))^(2) .

If z_1a n dz_2 are two complex numbers such that |z_1|=|z_2|a n d arg(z_1)+a r g(z_2)=pi , then show that z_1,=-( z )_2dot

CENGAGE ENGLISH-COMPLEX NUMBERS AND QUADRATIC EQUATIONS-All Questions
  1. If a ,b ,c are non zero complex numbers of equal modlus and satisfy a ...

    Text Solution

    |

  2. Column I, Column II If a ,b ,c ,a n dd are four zero real number...

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

  7. 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

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

  16. Let z1,z2, z3, zn be the complex numbers such that |z1|=|z2|=|zn|=1. I...

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

  19. Find the range of f(x)=x^2-x-3.

    Text Solution

    |

  20. If the fraction (x^3 +(a-10)x^2-x+a-6)/(x^3 +(a-6)x^2-x+a-10)reduces t...

    Text Solution

    |