Home
Class 11
MATHS
If x-iy = sqrt((a+ib)/(c-id)), prove tha...

If `x-iy = sqrt((a+ib)/(c-id))`, prove that `(x^(2) + y^(2))^(2) = (a^(2) + b^(2))/(c^(2) + d^(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 x+iy = (a+ib)/(a-ib) , prove that x^(2) + y^(2)=1 .

If x" - "i y" "=sqrt((a-i b)/(c-i d)) prove that (x^2+y^2)^2=(a^2+b^2)/(c^2+d^2)

If (a+ib)/(c+id)=x+iy prove that, (a^(2)+b^(2))/(c^(2)+d^(2))=x^(2)+y^(2)

If (a+ib)(c+id)(e+if)(g+ih) = A + iB , then show that (a^(2) + b^(2))(c^(2) + d^(2))(e^(2) + f^(2)) (g^(2) + h^(2)) = A^(2) + B^(2)

If xy=a[y+sqrt(y^(2)-x^(2))] , prove that, x^(3)(dy)/(dx)=y^(2)(y+sqrt(y^(2)-x^(2)))

If x+iy=((a+ib)/(c+id))^(1//2) ,show that (x^2+y^2)=(a^2+b^2)/(c^2+d^2)

If y - mx = sqrt(a^(2) m^(2) + b^(2)) and x + my = sqrt(a^(2) + b^(2) m^(2)) , then prove that x^(2) + y^(2) = a^(2) + b^(2)

If a : b = c : d , then prove that (a + c) : (b + d) = sqrt(a^(2) - c^(2)) : sqrt(b^(2) - d^(2))

If a/(y+z) = b/(z + x) = c/(x+y) , then prove that (a(b-c))/(y^(2)-z^(2)) = (b(c-a))/(z^(2)-x^(2)) = (c(a-b))/(x^(2)-y^(2)) .

If x : a = y : b = z : c , then prove that (a^(2) + b^(2) + c^(2))(x^(2) + y^(2) + z^(2)) = (ax + by + cz)^(2)

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

    |