Home
Class 11
MATHS
z1 and z2 be two complex no. then prove ...

`z_1` and `z_2` be two complex no. then prove that `abs(z_1+z_2)^2+abs(z_1-z_2)^2=2[abs(z_1)^2+abs(z_2)^2]`

Promotional Banner

Topper's Solved these Questions

  • COMPLEX NUMBER

    PATHFINDER|Exercise QUESTION BANK|224 Videos
  • CONIC SECTION

    PATHFINDER|Exercise QUESTION BANK|25 Videos

Similar Questions

Explore conceptually related problems

If z_1 and z_2 are two complex no. st abs(z_1+z_2) = abs(z_1)+abs(z_2) then

z_1 and z_2 are two different complex nos where z_1ne0 z_2ne0 prove that (abs(z_1)+abs(z_2))abs(z_1/abs(z_1)+(z_2)/(abs(z_2))) le 2(abs(z_1)+abs(z_2))

If z_1 and z_2 be two complex numbers such that abszle1, absz_2le1, abs(z_1+iz_2)=abs(z_1-iz_2)=2 , then z_1 equals

Prove that if z_1,z_2 are two complex numbers and cgt0 then abs((z_1+z_2)^2)le (1+c)abs((z_1)^2)+(1+(1/c))abs(z_2)^2

If z_(1) and z_(2) are two complex quantities, show that, |z_(1)+z_(2)|^(2)+|z_(1)-z_(2)|^(2)=2[|z_(1)|^(2)+|z_(2)|^(2)].

Let z_1 and z_2 are two complex nos s.t. abs(z_1) =abs(z_2)=1 then abs((z_1-z_2)/(1-z_1 barz_2)) is equal to

If z_1 and z_2 be two complex numbers such that abs(z_1+z_2)=abs(z_1) +abs(z_2) then the value of argz_1-argz_2 is equal to

If z_1 and z_2 be two complex numbers such that abs((z_1-2z_2)/(2-z_1barz_2))=1 and abs(z_2) ne1 , what is the value of abs(z_1) ?

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

PATHFINDER-COMPLEX NUMBERS-QUESTION BANK
  1. If omega is the imaginary cube root of 1 then prove that (a+bomega+com...

    Text Solution

    |

  2. If y=sqrt(x^2+6x+8) then show that one of the value of sqrt(1+iy)+sqrt...

    Text Solution

    |

  3. If x=cosalpha+isinalpha and 1+sqrt(1-y^2)=ny then show that y/2n(1+nx)...

    Text Solution

    |

  4. If a=1/2(5-isqrt3) then find the value of a^3-6a^2+12a-8

    Text Solution

    |

  5. Show that complex numbers (2+i3), (2-i3), (3-i2), (3+i2) are concyclic...

    Text Solution

    |

  6. If in argand plane the vertices A,B,C of an isoceles triangle are rep...

    Text Solution

    |

  7. If z1,z2,z3 are three complex number then prove that z1Im(barz2.z3)+z2...

    Text Solution

    |

  8. Prove that (1-omega^2)(1-omega^2+omega^4)(1-omega^4+omega^8)………..to 2n...

    Text Solution

    |

  9. If x-iy = sqrt((a+ib)/(c-id)), prove that (x^(2) + y^(2))^(2) = (a^(2)...

    Text Solution

    |

  10. If z be complex no. and (z-1)/(z+1) be purely imaginary show that z li...

    Text Solution

    |

  11. z1 and z2 be two complex no. then prove that abs(z1+z2)^2+abs(z1-z2)^2...

    Text Solution

    |

  12. If z=3/(2+costheta+isintheta) then show that z lies on a circle in the...

    Text Solution

    |

  13. If a=cosalpha+isinalpha , b=cosbeta+isinbeta , c=cosgamma+isingamma an...

    Text Solution

    |

  14. Ifomega is the imaginary cube root of unity and a+b+c=0 then show that...

    Text Solution

    |

  15. Ifz1,z2,z3 represent three vertices of an equilateral triangle in arga...

    Text Solution

    |

  16. Prove that the complex numbers z1,z2 and the origin from an isoceles t...

    Text Solution

    |

  17. If (1+x)^n=a0+a1x+a2x^2+…..+anx^n then show that (a0-a2+a4-……)^2+(a1-a...

    Text Solution

    |

  18. If z1,z2,z3………..zn are n complex numbers s.t, abs(z1)=abs(z2)=………….abs...

    Text Solution

    |

  19. z1 and z2 be two complex no. then prove that abs(z1+z2)^2+abs(z1-z2)^2...

    Text Solution

    |

  20. If costheta=1/2(a+1/a) cos(phi)=1/2(b+1/b) show that one of the valu...

    Text Solution

    |