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]`

A

`absz_2=1`

B

`z_2=0`

C

`absz_2=alpha`

D

`absz_2ltalpha`

Text Solution

Verified by Experts

The correct Answer is:
A
Promotional Banner

Topper's Solved these Questions

  • CIRCLE

    PATHFINDER|Exercise QUESTION BANK|198 Videos
  • COMPLEX NUMBERS

    PATHFINDER|Exercise QUESTION BANK|67 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 NUMBER-QUESTION BANK
  1. If abs(z-2-2i)=1, then the minimum value of absz is

    Text Solution

    |

  2. The point represented by the complex number 2-i is rotated about origi...

    Text Solution

    |

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

    Text Solution

    |

  4. For all complex numbers z1, z2 satisfying absz1=12 and abs(z2-3-4i)=5,...

    Text Solution

    |

  5. if z and w are two non-zero complex numbers such that absz=absw and ar...

    Text Solution

    |

  6. If z1, z2, z3, z4 represent the vertices of a rhombus in anticlockwise...

    Text Solution

    |

  7. If (x+iy)^7=a+ib, then (y+ix)^7 is equal to

    Text Solution

    |

  8. (1+i)^(n1)+(1+i^3)^(n1)+(1+i^5)^(n2)+(1+i^7)^(n2) is a real number if

    Text Solution

    |

  9. The value of underset(k=1)overset10sum(-sin((2kpi)/11)+icos((2kpi)/11)...

    Text Solution

    |

  10. If amp(z1z2)=0 and absz1=absz2=1, then

    Text Solution

    |

  11. if z1, z2, z3 are the vertices pf an equilateral triangle inscribed in...

    Text Solution

    |

  12. if amp (z-1)/(z+1)=pi/3, then the locus of z is

    Text Solution

    |

  13. If e^(ialpha)=cosalpha+isinalpha, then for the DeltaABC, the value of ...

    Text Solution

    |

  14. The equation zbarz+(4-3i)z+(4+3i)barz+5=0 represents a circle of radiu...

    Text Solution

    |

  15. Let z1 and z2 be two distinct complex numbers and let z= (1-t)z1+tz2 f...

    Text Solution

    |

  16. The roots of the equation Z^3+1=0 are called cube roots of unity.Clear...

    Text Solution

    |

  17. The roots of the equation Z^3+1=0 are called cube roots of unity.Clear...

    Text Solution

    |

  18. LetA(z1),B(z2) and C(z3) be the three points in Argands plane The po...

    Text Solution

    |

  19. LetA(z1),B(z2) and C(z3) be the three points in Argands plane The po...

    Text Solution

    |

  20. Match List - I with List-II

    Text Solution

    |