Home
Class 11
MATHS
If a+i b=((x+i)^2)/(2x^2+1), prove that ...

If `a+i b=((x+i)^2)/(2x^2+1),` prove that `a^2+b^2=((x^2+1)^2)/((2x^2+1)^2)`

Text Solution

AI Generated Solution

Promotional Banner

Topper's Solved these Questions

  • COMBINATIONS

    RD SHARMA ENGLISH|Exercise All Questions|117 Videos

  • DERIVATIVES

    RD SHARMA ENGLISH|Exercise All Questions|230 Videos

Similar Questions

Explore conceptually related problems

If a+i b=((x+i)^2)/(2x+1) , prove that a^2+b^2=((x+i)^2)/((2x+1)^2)

If a+bi= ((x+i)^(2))/(2x^(2)+1) , prove that a^(2) + b^(2)= ((x^(2) + 1)^(2))/((2x^(2) + 1)^(2))

If a+ib=(x+iy)/(x-iy) prove that a^2+b^2=1 and b/a=(2xy)/(x^2-y^2)

If x + i y =(a+i b)/(a-i b), prove that x^2+y^2=1 .

If a +ib = ((x+i)^(2))/(2x-1) then a^(2)+b^(2) is equal to

If x+i y=(a+i b)/(a-i b) 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 y=(cot^(-1)x)^2 , prove that y_2(x^2+1)^2+2x(x^2+1)y_1=2 .

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^2+1)^2)/(2a-i)=x+i y , then x^2+y^2 is equal to a. ((a^2+1)^4)/(4a^2+1) b. ((a+1)^2)/(4a^2+1) c. ((a^2-1)^2)/((4a^2-1)^2) d. none of these

RD SHARMA ENGLISH-COMPLEX NUMBERS-All Questions
  1. Find the multiplicative inverse of the complex number: 3+2i

    Text Solution

    |

  2. Find the multiplicative inverse of the following complex number: (2+sq...

    Text Solution

    |

  3. If a+i b=((x+i)^2)/(2x^2+1), prove that a^2+b^2=((x^2+1)^2)/((2x^2+1)^...

    Text Solution

    |

  4. 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...

    Text Solution

    |

  5. Find the least positive value of n if ((1+i)/(1-i))^n=1.

    Text Solution

    |

  6. Find real theta such that (3+2i\ sintheta)/(1-2i\ sintheta) is purely ...

    Text Solution

    |

  7. If (1+i)(1+2i)(1+3i)(1+n i)=(x+i y) , Show that 2.5.10 ..... (1+n^2)=x...

    Text Solution

    |

  8. Find the value of x^3+7x^2-x+1,\ w h e n\ x=1+2idot

    Text Solution

    |

  9. Prove that: x^4+4=(x+1+i)(x+1-i)(x-1+i)(x-1-i).

    Text Solution

    |

  10. Show that a real value of x\ will satisfy the equation (1-ix)/(1+ix)=...

    Text Solution

    |

  11. If alpha an d beta are different complex numbers with |beta|=1,then ...

    Text Solution

    |

  12. Find non zero integral solutions of |1-i|^x=2^xdot

    Text Solution

    |

  13. Express the following complex numbers in the standard form a+i b :(1+i...

    Text Solution

    |

  14. Express the following complex numbers in the standard form a+i b :1/((...

    Text Solution

    |

  15. Express the following complex numbers in the standard form a+i b :((2+...

    Text Solution

    |

  16. Express the following complex numbers in the standard form a+i b :(1+2...

    Text Solution

    |

  17. Express the following complex numbers in the standard form a+i b :(1/(...

    Text Solution

    |

  18. Express the following complex numbers in the standard form a+i b :(3+2...

    Text Solution

    |

  19. Express the following complex numbers in the standard form a+i b :(1-i...

    Text Solution

    |

  20. Express the following complex numbers in the standard form a+i b :((1+...

    Text Solution

    |