Home
Class 12
MATHS
For any two complex numbers, z(1),z(2) a...

For any two complex numbers, `z_(1),z_(2)` and any two real numbers a and b, `|az_(1)-bz-(2)|^(2)+|bz_(1)+az_(2)|^(2)=`

A

`(a+b)(|z_(1)|^(2)+|z_(2)|^(2))`

B

`(a^(2)+b^(2))(|z_(1)|^(2)+|z_(2)|^(2))`

C

`(a^(2)+b^(2))(|z_(1)|+|z_(2)|)`

D

none of these

Text Solution

Verified by Experts

The correct Answer is:
B
Promotional Banner

Topper's Solved these Questions

  • COMPLEX NUMBERS

    OBJECTIVE RD SHARMA|Exercise Chapter Test|59 Videos

  • COMPLEX NUMBERS

    OBJECTIVE RD SHARMA|Exercise Section II - Assertion Reason Type|15 Videos

  • CIRCLES

    OBJECTIVE RD SHARMA|Exercise Chapter Test|55 Videos

  • CONTINUITY AND DIFFERENTIABILITY

    OBJECTIVE RD SHARMA|Exercise Exercise|86 Videos

Similar Questions

Explore conceptually related problems

For any two complex numbers z_(1),z_(2) and any real numbers a and b,|az_(1)-bz_(2)|^(2)+|bz_(1)+az_(2)|^(2)=...

Fill in the blanks of the following . (i) For any two complex numbers z_(1), z_(2) and any real numbers a, b, |az_(1) - bz_(2)|^(2) + |bz_(1) + az_(2)|^(2) =* * * (ii) The value of sqrt(-25) xxsqrt(-9) is … (iii) The number (1 - i)^(3)/(1 -i^(3)) is equal to ... (iv) The sum of the series i + i^(2) + i^(3)+ * * * upto 1000 terms us ... (v) Multiplicative inverse of 1 + i is ... (vi) If z_(1) "and" z_(2) are complex numbers such that z_(1) + z_(2) is a real number, then z_(1) = * * * (vii) arg(z) + arg barz "where", (barz ne 0) is ... (viii) If |z + 4| le 3, "then the greatest and least values of" |z + 1| are ... and ... (ix) If |(z - 2)/(z + 2)| =(pi)/(6) , then the locus of z is ... (x) If |z| = 4 "and arg" (z) = (5pi)/(6), then z = * * *

For any two complex numbers z_(1) and z_(2) and any two real numbers a,b find the value of |az_(1)-bz_(2)|^(2)+|az_(2)+bz_(1)|^(2)

If z_(1) and z_(2) are two complex number and a, b,are two real number then |az_(1)-bz_(2)|^(2)+|bz_(1)+az_(2)|^(2) equals

For any two complex numbers z_(1),z_(2) the values of |z_(1)+z_(2)|^(2)+|z_(1)-z_(2)|^(2) , is

For any two complex numbers z_(1) and z_(2) prove that: |backslash z_(1)+z_(2)|^(2)+|backslash z_(1)-z_(2)|^(2)=2[|backslash z_(1)|^(2)+|z_(2)|^(2)]

Fill in the blanks . If z_1 and z_2 are two complex numbers such that a,b,|az_(1) - bz_(2) |^(2) + |bz_(1) + az_(2)|^(2) = …

OBJECTIVE RD SHARMA-COMPLEX NUMBERS -Exercise
  1. The equation barbz+b barz=c, where b is a non-zero complex constant an...

    Text Solution

    |

  2. If |a(i)| lt 1, lambda(i) ge 0 for i=1,2,……n and lambda(1)+lambda(2)+…...

    Text Solution

    |

  3. For any two complex numbers, z(1),z(2) and any two real numbers a and ...

    Text Solution

    |

  4. Common roots of the equation z^(3)+2z^(2)+2z+1=0 and z^(2020)+z^(2018)...

    Text Solution

    |

  5. If z(1) and z(2) are two complex numbers such that |(z(1)-z(2))/(1-bar...

    Text Solution

    |

  6. The points representing cube roots of unity

    Text Solution

    |

  7. If z(1) and z(2) are two complex numbers such that |(z(1)-z(2))/(z(1)+...

    Text Solution

    |

  8. If z(1), z(2) are two complex numbers such that |(z(1)-z(2))/(z(1)+z(2...

    Text Solution

    |

  9. If n is a positive integer greater than unity z is a complex number sa...

    Text Solution

    |

  10. If n is a positive integer greater than unity z is a complex number sa...

    Text Solution

    |

  11. If at least one value of the complex number z=x+iy satisfies the condi...

    Text Solution

    |

  12. Given z is a complex number with modulus 1. Then the equation [(1+i a)...

    Text Solution

    |

  13. The center of a regular polygon of n sides is located at the point z=0...

    Text Solution

    |

  14. If the points z(1),z(2),z(3) are the vertices of an equilateral triang...

    Text Solution

    |

  15. For any complex number z, the minimum value of |z|+|z-1|

    Text Solution

    |

  16. The inequality |z-4| < |z-2| represents

    Text Solution

    |

  17. Number of non-zero integral solution of the equation |1-i| ^(n)=2^(n),...

    Text Solution

    |

  18. If "Im"(2z+1)/(iz+1)=-2, then locus of z, is

    Text Solution

    |

  19. lf z(!=-1) is a complex number such that [z-1]/[z+1] is purely imagina...

    Text Solution

    |

  20. If x=-5+2sqrt(-4) , find the value of x^4+9x^3+35 x^2-x+4.

    Text Solution

    |