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

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

Promotional Banner

Topper's Solved these Questions

  • MODEL PAPER (14)

    JBD PUBLICATION|Exercise EXERCISE|39 Videos

  • MODEL PAPER (2)

    JBD PUBLICATION|Exercise EXERCISE|41 Videos

Similar Questions

Explore conceptually related problems

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

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

If 1 +4 sqrt3i = (a+ ib)^2 , prove that : a^2-b^2=1 and ab=2 sqrt3 .

If y = log (x + sqrt(x^2+1))/(sqrt(x^2+1)) , prove that (x^2 +1) dy/dx + xy = 1

If x+iy=(a+ib)/(a-ib) , then prove that x^2+y^2=1

If y = tan^-1((e^(2x) +1)/(e^(2x) -1)) , prove that : dy/dx =-(2e^(2x))/(1+e^4x)

If y = (sin^-1x)/(sqrt(1-x^2)) , prove that (1-x^2)(dy/dx)- xy = 1

If y = (tan^-1 x)^2 , then prove that (1+x^2)^2 (d^2y)/(dx^2) + 2x(1+x^2)dy/dx - 2 = 0

If y= (cos^-1 x)^2 , prove that: (1 - x^2 ) ((d^2y)/dx^2) - x(dy/dx) -2 = 0 .

JBD PUBLICATION-MODEL PAPER (15)-EXERCISE
  1. Prove that A^c-B^c=B-A.

    Text Solution

    |

  2. If f(x)=log(x/(x-1)), show that f(x+1)+f(x)=log ((x+1)/(x-1))

    Text Solution

    |

  3. Prove that:cos15^@-sin15^@=1/sqrt2

    Text Solution

    |

  4. Prove that : cos 24^@+ cos 55^@ + cos 125^@ + cos204^@ + cos 300^@= 1/...

    Text Solution

    |

  5. How many words, with or without meaning, each of 2 vowels and 3 conson...

    Text Solution

    |

  6. Find the value of n such that : "^nP5=42 ^nP3, n>4.

    Text Solution

    |

  7. Sum of first p,q and r terms of an A.P. are a,b,c respectively. Prove...

    Text Solution

    |

  8. If the angle between two lines is pi/3 and slope of one of the line is...

    Text Solution

    |

  9. If a parabolic reflector is 20 cm in diameter and 50 cm deep. Find the...

    Text Solution

    |

  10. Evaluate: underset(xrarr1)lim ((x+x^2+x^3+……….x^n)-n)/(x-1)

    Text Solution

    |

  11. If y=asinx+bcosx, prove thaty^2+((dy)/(dx))^2=a^2+b^2

    Text Solution

    |

  12. A,B and C are three mutually exclusive and exhaustive events associat...

    Text Solution

    |

  13. Find theta such that (3+2i sin theta)/(1-2i sin theta) is purely real.

    Text Solution

    |

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

    Text Solution

    |

  15. Solve the following system of inequalities graphically: 4x + 3y le 60,...

    Text Solution

    |

  16. IQ of a person is given by the formula IQ= (MA)/(CA)xx100 , where MA i...

    Text Solution

    |

  17. Evaluate: underset(xrarr0)lim (sqrt(1+2x)-sqrt(1-2x))/(x)

    Text Solution

    |

  18. Find the derivative of cos x w.r.t. x

    Text Solution

    |

  19. Find the mean marks from the following data :

    Text Solution

    |

  20. Find the mean deviation from the mean for the following data. 38, 70, ...

    Text Solution

    |