Home
Class 12
MATHS
If the complex numbers z1, z2,.......zn ...

If the complex numbers `z_1, z_2,.......z_n` lie on te unit circle |z| = 1 then show that `|z_1 + z_2 + ..... + z_n| = |z_1^(-1)1 + z_2^(-1) + ....... + z_n^(-1)|.`

Promotional Banner

Topper's Solved these Questions

  • COMPLEX NUMBERS

    A DAS GUPTA|Exercise EXERCISE|224 Videos

  • Circular Functions, Identities

    A DAS GUPTA|Exercise Exercise|300 Videos

  • Continuity, Differentiability and Graph of Function

    A DAS GUPTA|Exercise Exercise|38 Videos

Similar Questions

Explore conceptually related problems

If two complex numbers z_(1),z_(2) are such that |z_(1)|=|z_(2)| , is it then necessary that z_(1)=z_(2) ?

For complex number z,|z-1|+|z+1|=2 then z lies on

If two complex numbers z_(1) and z_(2) are such that |z_(1)|=|z_(2)| , is it then necessary that z_(1)=z_(2) ?

If the complex number Z_(1) and Z_(2), arg (Z_(1))- arg(Z_(2)) =0 . then show that |z_(1)-z_(2)| = |z_(1)|-|z_(2)| .

If z_(1),z_(2),……………,z_(n) lie on the circle |z|=R , then |z_(1)+z_(2)+…………….+z_(n)|-R^(2)|1/z_(1)+1/z_(2)+…….+1/z-(n)| is equal to

If for complex numbers z_(1) and z_(2)arg(z_(1))-arg(z_(2))=0, then show that |z_(1)-z_(2)|=|z_(1)|-|z_(2)||

If z_1 and z_2 are two complex numbers, then prove that |z_1 - z_2|^2 le (1+ k)|z_1|^2 +(1+K^(-1) ) |z_2|^2 AA k in R^(+) .

A DAS GUPTA-COMPLEX NUMBERS-EXERCISE
  1. If (a1+ib1)(a2+ib2)...(an+ibn) = x+iy , prove that : (a1^2+b1^2)(a2^2+...

    Text Solution

    |

  2. If (a1+ib1)(a2+ib2)...(an+ibn) = x+iy , prove that : tan^-1frac(b1)(a1...

    Text Solution

    |

  3. If the complex numbers z1, z2,.......zn lie on te unit circle |z| = 1 ...

    Text Solution

    |

  4. Show that if iz^3+z^2-z+i=0, then |z|=1

    Text Solution

    |

  5. If f(z) = a0z^n+a1z^(n-1)+a2z^(n-2)+...+an where z is a complex numbe...

    Text Solution

    |

  6. If |z1+z2| = |z1-z2|, prove that ampz1 - ampz2 = pi/2 .

    Text Solution

    |

  7. Prove that |z1+z2|^2 = |z1|^2+|z2|^2 if z1/z2 is purely imaginary.

    Text Solution

    |

  8. Prove that |z1+z2|^2+|z1-z2|^2 =2|z1|^2+2|z2|^2.

    Text Solution

    |

  9. Prove that |alpha+sqrt(alpha^2-beta^2)|+|alpha-sqrt(alpha^2-beta^2)|= ...

    Text Solution

    |

  10. Prove that |1-barz1z2|^2-|z1-z2|^2=(1-|z1|^2)(1-|z2|^2).

    Text Solution

    |

  11. If |z-1| <3, prove that |iz+3-5i| < 8.

    Text Solution

    |

  12. Prove that for nonzero complex numbers |z1+z2| |frac(z1)(|z1|)+frac(z2...

    Text Solution

    |

  13. Prove that following inequalities: (i) |(z)/(|z|) -1| le |arg z| (...

    Text Solution

    |

  14. Find the value of w^4+w^6+w^8, if w is a complex cube root of unity.

    Text Solution

    |

  15. Find the range of real number alpha for which the equation z+alpha|z-1...

    Text Solution

    |

  16. If a, b are real, prove that the equation z^2+az+b=0 will not have any...

    Text Solution

    |

  17. Find the maximum and minimum values of |z| satisfying |z+(1)/(z)|=2

    Text Solution

    |

  18. If |z|ge3, then determine the least value of |z+(1)/(z)|.

    Text Solution

    |

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

    Text Solution

    |

  20. Locate the region in the Argand plane for the complex number z satisfy...

    Text Solution

    |