Home
Class 11
MATHS
If ((a^2+1)^2)/(2a-i)=x+i y , then x^2+y...

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

Text Solution

AI Generated Solution

To solve the problem, we start with the given equation: \[ \frac{(a^2 + 1)^2}{2a - i} = x + iy \] We want to find \(x^2 + y^2\). ...
Promotional Banner

Topper's Solved these Questions

  • COMBINATIONS

    RD SHARMA|Exercise Solved Examples And Exercises|117 Videos

  • DERIVATIVES

    RD SHARMA|Exercise Solved Examples And Exercises|236 Videos

Similar Questions

Explore conceptually related problems

If x+ iy=(1+ 4i)(1+5i) , then (x^(2)+y^(2)) is equal to :

int(x)/(4+x^(4))dx is equal to (1)/(4)tan^(-1)x^(2)(b)(1)/(4)tan^(-1)((x^(2))/(2))(c)(1)/(2)tan^(-1)((x^(2))/(2))(d) none of these

If (1-i)x+(1+i)y=1-3i , then (x,y) is equal to (a) (2,-1) (b) (-2,1) (c) (-2,-1) (d) (2,1)

If (1-i)x+(1+i)y=1-3i , then (x,y) is equal to (a) (2,-1) (b) (-2,1) (c) (-2,-1) (d) (2,1)

If 2^(2x-1)+4^(x)=2^(x-(1)/(2))+2^(x+(1)/(2)), then x equals a.(1)/(2) b.(2)/(3) c.1 d.(3)/(2)

If y=(sin^(-1)x)^(2), then (1-x^(2))y_(2) is equal to xy_(1)+2(b)xy_(1)-2(c)xy_(1)+2(d) none of these

None of these int(2x)/((1-x^(2))sqrt(x^(4)-1))dx is equal to :( A) sqrt((x^(2)-1)/(x^(2)+1))+c(B)sqrt((x^(2)+1)/(x^(2)-1))(C)sqrt(x^(4)+1)(D) None of these

intdx/(sqrt(x)(1+x^2)^(5/4))= (A) (2x)/(1+x^2)^(1/4)+c (B) (2sqrt(x))/(1+x^2)^(1/4)+c (C) (2sqrt(x))/(1+x^2)+c (D) none of these

The equation of the hyperbola whose foci are (6,4) and (-4,4) and eccentricity 2 is ((x-1)^(2))/(25/4)-((y-4)^(2))/(75/4)=1b((x+1)^(2))/(25/4)-((y+4)^(2))/(75/4)=1c((x-1)^(2))/(75/4)-((y-4)^(2))/(25/4)=1d .none of these

RD SHARMA-COMPLEX NUMBERS-Solved Examples And Exercises
  1. If a=costheta+isintheta, then (1+a)/(1-a) is a. cot(theta/2) b. cot...

    Text Solution

    |

  2. If (1+i)(1+2i)(1+3i)...(1+n i)=a+i b , then 2. 5. 10. 17... (1+n^2\ )...

    Text Solution

    |

  3. If ((a^2+1)^2)/(2a-i)=x+i y , then x^2+y^2 is equal to a. ((a^2+1)^4)/...

    Text Solution

    |

  4. The principal value of the argument of (1+i) is A. pi B. pi/(12) C....

    Text Solution

    |

  5. The least positive integer n such that ((2i)/(1+i))^n is a positive in...

    Text Solution

    |

  6. If z is a non zero complex, number then |(|barz |^2)/(z barz )| is eq...

    Text Solution

    |

  7. If a=1+i , then a^2 equals A. 1-i B. 2i C. (1+i)(1-i) D. (i-1)

    Text Solution

    |

  8. If (x+i y)^(1//3)=a+i b ,\ then\ x/a+y/b is a. 0 b. 1 c. -1 d. none o...

    Text Solution

    |

  9. (sqrt(-2))(sqrt(-3)) is equal to A. sqrt(6) B. -sqrt(6) C. isqrt(6)...

    Text Solution

    |

  10. The argument of (1-isqrt(3))/(1+isqrt(3)) is a. 60^@ b. 120^@ c. 210^@...

    Text Solution

    |

  11. If z=((1+i)/(1-i)), then z^4 equals a. 1 b. -1 c. 0 d non of t...

    Text Solution

    |

  12. If z=(1+2i)/(1-(1-i)^2), then arg(z) equals a. 0 b. pi/2 c. pi ...

    Text Solution

    |

  13. If z=1/((2+3i)^2), then |z| is a. 1/13 b. 1/5 c. 1/12 d. n...

    Text Solution

    |

  14. If z=1/((1-i)(2+3i)), then |z| is a. 1 b. 1/sqrt(26) c. 5/sqrt(...

    Text Solution

    |

  15. If z=1-costheta+isintheta,\ t h e n\ |z| is a. 2sin(theta/2) b. 2cos(t...

    Text Solution

    |

  16. If x+i y=(1+i)(1+2i)(1+3i),\ t h e n\ x^2+y^2 is a. 0 b. 1 c. 100 d. n...

    Text Solution

    |

  17. If z=1/(1-cos theta-i sin theta), then Re(z) is a. 0 b. 1/2 c. c...

    Text Solution

    |

  18. If x+i y=(3+5i)/(7-6i), then y is

    Text Solution

    |

  19. The amplitude of 1/i is equal to-

    Text Solution

    |

  20. The argument of (1-i)/(1+i) is-

    Text Solution

    |