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

  • BINOMIAL THEOREM

    CENGAGE ENGLISH|Exercise All Questions|365 Videos

  • CONIC SECTIONS

    CENGAGE ENGLISH|Exercise All Questions|1344 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

CENGAGE ENGLISH-COMPLEX NUMBERS AND QUADRATIC EQUATIONS-All Questions
  1. Show that a real value of x will satisfy the equation (1-i x)//(1+i x)...

    Text Solution

    |

  2. Prove that the roots of the equation (a^4+b^4)x^2+4a b c dx+(c^4+d^4)=...

    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 the roots of the equation x^2-8x+a^2-6a=0 are real distinct, then f...

    Text Solution

    |

  5. Solve :z^2+|z|=0 .

    Text Solution

    |

  6. If roots of equation x^2-2c x+a b=0 are real and unequal, then prove ...

    Text Solution

    |

  7. Find the range of real number alpha for which the equation z+alpha|z-1...

    Text Solution

    |

  8. If the roots of the equation a(b-c)x^2+b(c-a)x+c(a-b)=0 are equal, sho...

    Text Solution

    |

  9. If (1+i)^2 /(3 - i) , then Re(z) =

    Text Solution

    |

  10. Find the quadratic equation with rational coefficients whose one root ...

    Text Solution

    |

  11. Let z be a complex number satisfying the equation (z^3+3)^2=-16 , then...

    Text Solution

    |

  12. If f(x)=a x^2+b x+c ,g(x)=-a x^2+b x+c ,where ac!=0, then prove that f...

    Text Solution

    |

  13. Find the real numbers x and y if (x-i y)(3+5i) is the conjugate of ...

    Text Solution

    |

  14. If x is real, then x//(x^2-5x+9) lies between -1a n d-1//11 b. 1a n d-...

    Text Solution

    |

  15. Find the least positive integer n such that ((2i)/(1+i))^n is a positi...

    Text Solution

    |

  16. Set of all real value of a such that f(x)=((2a-1)x^2+2(a+1)x+(2a-1))/(...

    Text Solution

    |

  17. Find the real part of e^e^(itheta)

    Text Solution

    |

  18. If alpha, beta and gamma are the roots of x^3 - x^2-1 = 0, then value ...

    Text Solution

    |

  19. Prove that z=i^i, where i=sqrt-1, is purely real.

    Text Solution

    |

  20. If alpha,beta,gamma,delta are the roots of the equation x^4-K x^3+K x...

    Text Solution

    |